All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 4 Lesson 6 Problem-Solving Investigation: Solve a Simpler Problem will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 4 Lesson 6 Problem-Solving Investigation: Solve a Simpler Problem
Learn the Strategy
Miguel earns $50 each week. He spends $10 each week and saves the remaining amount. How many weeks will it take until he has saved more than $300?
1. Understand
What facts do you know?
I know that Miguel earns ____________ each week, but spends ______________ of it.
What do you need to find?
I need to find how long it will take Miguel to save _____________.
2. Plan
I can solve the problem by solving a simpler problem.
3. Solve
Miguel saves $50 – $10, or ____________ each week.
Divide 300 ÷ 40. Since there is a remainder,
Miguel will need to save for at least ____________ weeks.
4. Check
Is my answer reasonable? Explain.
Yes. _____________ × 8 = _____________, and ____________ is greater than $300.
Answer: Given that,
(i) What facts do you know?
I know that Miguel earns $50 each week, but spends $10 of it.
What do you need to find?
I need to find how long it will take Miguel to save $300.
(ii) I can solve the problem by solving a simpler Problem.
(iii) Miguel saves $50 – $10, or $40 each week.
Divide 300 ÷ 40.
Since there is a remainder, 7 R 20 i.e., approximately equal to 8.
Miguel will need to save for at least 8 weeks.
(iv) Yes. $40 x 8 = $320, and $360 is greater than $300.
Practice the Strategy
Melissa estimates that she watched 104 movies over the past year. On average, about how many movies does she watch per month? (hint: 1 year = 52 weeks)
1. Understand
What facts do you know?
What do you need to find?
2. Plan
3. Solve
4. Check
Is my answer reasonable? Explain.
Answer: Given that,
(i) Melissa watched 104 movies last year.
We will find, out how many movies she watches per month.
(ii) You can solve the problem by solving a simpler problem.
(iii) First, find how many movies Melissa watched per week.
104 / 52 = 2 (1 year = 52 weeks)
So, Melissa watched 2 movies per week.
Now, determine the number of movies she watched each month.
Multiply the number of movies watched per week by 4 since there are 4 weeks in each month.
then it is, 4 x 2 = 8 movies.
Hence, Melissa watched about 8 movies each month last year.
(iv) Yes. 8 x 12 = 96. The 96 is about 104.
Apply the Strategy
Solve each problem by solving a simpler problem.
Question 1.
Mr. Santiago has a flight from New York to Paris that covers a distance of 3,640 miles in 7 hours. If the plane travels at the same speed per hour, how many miles will it have traveled after 4 hours?
Answer: It has traveled 2080 miles after 4 hours.
Explanation: As given in the question,
Mr. Santiago has a flight from New York to Paris that covers a distance of 3,640 miles in 7 hours.
If the plane travels at the same speed per hour.
Then find out how many miles will it have traveled after 4 hours.
Now, we will find the miles.
So, the values are 3640 and 7. Divide the given values.
For 1 hour he traveled 520 miles. So, for 7 hours he traveled 4 x 520 = 2080 miles.
Hence, it traveled 2080 miles after 4 hours.
Question 2.
Josh watches 720 television shows in one year. If he watches the same number of shows each month, how many shows does he watch in 5 months?
Answer: 300 shows Josh watched in 5months.
Explanation: Given that,
Josh watches 720 television shows in one year.
If he watches the same number of shows each month.
Then find out how many shows he watch in 5 months.
The values are 720 and one years (12 months). Now, divide it.
For one month 60 shows he watched.
Now, find out how many shows he watched in 5 months.
i.e., 5 x 60 = 300 shows.
Hence, josh watched 300 shows in 5months.
Question 3.
The football team is raising money to have a new turf field installed. The cost of the turf field is $48,780. The team has 18 months to raise the money. If they raise an equal amount each month, how much will they have raised after one year?
Answer: If they raise an equal amount each month, $32520 will they have raised after one year.
Explanation: As given in the question, the data is
The football team is raising money to have a new turf field installed.
The cost of the turf field is $48,780.
The team has 18 months to raise the money.
If they raise an equal amount each month, then find out how much will they have raised after one year.
So, the values for division is 48780 and 18. The division process is,
For 1month the money is 2710. From that, 12 months is 12 x 2710 = 32520 (1 year = 12months)
Hence, $32520 will they have raised after one year.
Question 4.
Mathematical PRACTICE Keep Trying The Clearview Window Washing Company has a contract to wash 3,082 windows on a 23-story building. The company will wash the windows on the first three floors on the first day. If there are the same number of windows on each floor, how many windows will the company wash on the first day?
Answer: 402 windows will the company wash on the first day.
Explanation: Given that,
The Clearview Window Washing Company has a contract to wash 3,082 windows on a 23-story building.
The company will wash the windows on the first three floors on the first day.
If there are the same number of windows on each floor.
Then how many windows will the company wash on the first day.
So the values are 3082 and 23. Now divide it.
Each floor consists of 134 windows. In three floors the windows are, 134 x 3 = 402.
Hence, 402 windows will the company wash on the first day.
Question 5.
Mr. Thomas is delivering bricks to a construction site. He delivers the same number of bricks with each delivery. The builder has ordered 3,096 bricks and it will take 8 trips to deliver all the bricks. How many bricks will Mr. Thomas have delivered after 7 trips?
Answer: 2709 bricks will Mr.Thomas had delivered after 7 trips.
Explanation: As given the data,
Mr. Thomas is delivering bricks to a construction site.
He delivers the same number of bricks with each delivery.
The builder has ordered 3,096 bricks and it will take 8 trips to deliver all the bricks.
Now, find out how many bricks will Mr. Thomas have delivered after 7 trips.
So, the values are 3096 and 8.
After division, one trip consists of 387 bricks.
Then for 7 trips = 7 x 387 = 2709 bricks.
Therefore, 2709 bricks will Mr.Thomas had delivered after 7 trips.
Review the Strategies
Use any strategy to solve each problem.
- Solve a simpler problem.
- Determine extra or missing information.
- Make a table.
- Use the four-step plan.
Question 6.
An aquarium at a pet store has 18 Black Neon Tetra fish in it. A customer buys 12 Black Neon Tetra fish at the same time the store clerk adds 7 more Black Neon Tetra fish to the tank. How many Black Neon Tetra fish are in the aquarium now?
Answer: Now, 13 Black Neon Tetra fishes are there in the Aquarium.
Explanation: As given in the question,
A pet store an aquarium consists of 18 Black Neon Tetra fishes.
A customer buy 12 fishes.
So, the remaining fishes are, 18 – 12 = 6.
At the same time the store clerk add 7 more fishes.
At present, the total number of Black Neon Tetra fishes in the aquarium is, 6 + 7 = 13.
Question 7.
Kolby read 108 books in one year. If he reads the same number of books each month, how many books does he read in 5 months?
Answer: Kolby reads 45 books in 5months.
Explanation: As given in the question,
Kolby read 108 books in one year.
If he reads the same number of books each month, then number of books does he read in 5 months.
We know that, 1 year = 12 months.
So, divide the books by 12 to get the value is 108/12 = 9.
Each month reads 9 months.
Therefore, in 5 months he reads 5 x 9 = 45. Hence, Kolby reads 45 books.
Question 8.
Mr. Reyes baked 4 batches of muffins for his class. Each batch had 12 muffins. If Mr. Reyes has 24 students, how many muffins will each student receive?
Answer: 2 muffins will each students receive.
Explanation: Given that,
Mr. Reyes baked 4 batches of muffins for his class.
Each batch had 12 muffins.
If Mr. Reyes has 24 students, then how many muffins will each student receive.
So, the total muffins are 4 x 12 = 48.
The number of students are 24 and the total muffins are 48.
Now divide 48 by 24.
i.e., 48/24 = 2.
Hence, each student receive 2 muffins.
Question 9.
The quotient of two numbers is 20. Their sum is 84. What are the 2 numbers?
Answer: The two numbers are 80 and 4.
Explanation: Given that,
The quotient of two numbers is 20.
The sum is 84.
So, the two numbers are 80 and 4.
Because the sum is 80 + 4 = 84.
The quotient is 80/4 = 20
Therefore, the two numbers are 80 and 4.
Question 10.
Mathematical PRACTICE Model Math Charity and her friend each want to buy a piece of pizza, a drink, and an ice cream cone. Charity has $10 to pay for her and her friend’s meal. Does she have enough money? Explain.
Answer: No, she does not have enough money. Because she has only 10 dollars.
Explanation: Given that,
Charity and her friend each want to buy a piece of pizza, a drink, and an ice cream cone.
Charity has $10 to pay for her and her friend’s meal.
Now, find out her money is enough or not.
For one the total price is,
pizza+ drink + ice cream zone = 3 + 1+ 2 = 6.
So, for 2 person the total price is 12. Thatswhy $10 is not enough.
McGraw Hill My Math Grade 5 Chapter 4 Lesson 6 My Homework Answer Key
Problem Solving
Solve each problem by solving a simpler problem.
Question 1.
Harold stores 10,656 pounds of grain for his 24 cattle. Each cow eats about 12 pounds of grain each day. How many days would the food supply last?
Answer: 37 days would the food supply last.
Explanation: Given that,
Harold stores 10,656 pounds of grain for his 24 cattle.
Each cow eats about 12 pounds of grain each day.
Therefore if one cow eat 12 pounds a day then 24 cows is, 12 x 24 = 288 pounds of a day.
Now, we will find out number of days would the food supply last.
So, 1 day = 288 pounds.
Divide 10656by 288, to get
Hence, the number of days that the food supply would last is 37 days.
Question 2.
Mathematical PRACTICE Make Sense of Problems The Pave the Way Company is installing a new walkway. The installer uses 13 paving stones for every foot of walkway. He needs 117 paving stones to complete the project and has used 78 paving stones so far. How many more feet of paving stones will he need to install to finish?
Answer: 3 more feets of paving stones are needed to finish the installing.
Explanation: Given that,
The Pave the Way Company is installing a new walkway.
The installer uses 13 paving stones for every foot of walkway.
He needs 117 paving stones to complete the project and has used 78 paving stones so far.
Now, find how many more feet of paving stones will he needed to install to finish.
So, the values are 117, 78. Now subtract it.
117-78 = 39.
Divide 39 by 13. To get the final value.
39/13 = 3 feet.
So, 3 more feets of paving stones are needed to finish the installing.
Question 3.
Harvey collects rare marbles. He has 112 marbles in his collection. Each tray holds an equal number of marbles. If he uses 7 trays to hold all of the marbles, how many marbles will he display on 3 trays?
Answer: There are 48 marbles displayed on three trays.
Explanation: As given in the question,
Harvey collects 112 rare marbles in his collection.
Each tray holds an equal number of marbles.
If he uses 7 trays to hold all of the marbles, then how many marbles will he display on 3 trays.
Now, we will find the marbles value.
The dividing values are 112 and 7.
112/7 = 16
So, number of marbles displays on 3 trays is, 3 x 16 = 48.
Therefore, 48 marbles displayed on three trays.
Question 4.
Noelle’s rectangular deck has a length of 18 feet and a width of 16 feet. If a hot tub takes up a square that is 4 feet on each side in the middle of the deck, how much area is left of the deck?
Answer: 272 square feets area is left of the deck
Explanation: As given in the question,
Noelle’s rectangular deck has a length of 18 feet and a width of 16 feet.
If a hot tub takes up a square that is 4 feet on each side.
In the middle of the deck, how much area is left of the deck?
Now, we will find that area.
The formula for area of a rectangle is, A = l x w.
So, the area of a rectangle is, A = 18 x 16 = 288 square feets.
Next, find the area of a hot tub.
The formula for area of a square is A = 4s.
The area of a hot tub is, A = 4 x 4 = 16 square feets.
Now, find the difference of both area.
The areas is 288 – 16 = 272 square feets.
So, the left area of the deck is 272 square feets.
Question 5.
Hilary wants to go on the Latin Club trip to Italy. It will cost $2,730 for the trip. The trip is 30 weeks away and she wants to make equal weekly payments. How much money altogether does Hilary need to pay at the end of week 8?
Answer: $728 altogether Hilary need to pay at the end of week 8.
Explanation: Given that,
Hilary wants to go on the Latin Club trip to Italy.
It will cost $2,730 for the trip.
The trip is 30 weeks away and she wants to make equal weekly payments.
Now, we will find out how much money altogether does Hilary need to pay at the end of week 8.
The values are 2730 and 30. Divide the given values.
The quotient value is 91. It means per week $91.
So, for 8 weeks it is 8 x 91 = $728.
Therefore, Hilary needs to pay $728 for 8weeks.
Fluency Practice
Question 1.
Answer: The quotient value is 36.
Explanation: Given that, the values are 432 and 12.
Now we will find the quotient value.
After division the quotient value is 36.
Question 2.
Answer: The quotient value is 21 R 10.
Explanation: Given that, the values are 850 and 40.
Now we will find the quotient value.
After division the quotient value is 21 R 10.
Question 3.
Answer: The quotient value is 17.
Explanation: Given that, the values are 493 and 29.
Now we will find the quotient value.
After division the quotient value is 17.
Question 4.
Answer: The quotient value is 29 R 13.
Explanation: Given that, the values are 535 and 18.
Now we will find the quotient value.
After division the quotient value is 29 R 13.
Question 5.
Answer: The quotient value is 3 R 9.
Explanation: Given that, the values are 105 and 32.
Now we will find the quotient value.
After division the quotient value is 3 R 9.
Question 6.
Answer: The quotient value is 14 R 29.
Explanation: Given that, the values are 897 and 62.
Now we need to find the quotient value.
After division to get the quotient value is 14 R 29.
Question 7.
Answer: The quotient value is 7.
Explanation: Given that, the values are 504 and 72.
Now we will find the quotient value.
After division the quotient value is 7.
Question 8.
Answer: The quotient value is 13.
Explanation: Given that, the values are 689 and 53.
Now, we need to find the quotient value.
After division, to get the quotient value is 13.
Question 9.
Answer: The quotient value is 6.
Explanation: Given that, the values are 126 and 21.
Now, we need to find the quotient value.
The below is the division process,
By dividing 126 and 21. To get the quotient value is 6.
Question 10.
Answer: The quotient value is 12 R 8.
Explanation: Given that, the values are 452 and 37.
Now, we need to find the quotient value.
After division to get the quotient value is 12 R 8.
Question 11.
Answer: The given values quotient is 9.
Explanation: Given that, the values are 684 and 76.
Now, we will find the quotient value.
The division process is,
After division the quotient value is 9.
Question 12.
Answer: The quotient value is 4 R 5
Explanation: Given that, the values are 209 and 51.
Now, we need to find the quotient value.
After division the quotient value is 4 R 5.
Question 13.
Answer: The quotient value is 14.
Explanation: Given that, the values are 938 and 67.
Now we will find the quotient value.
After division, to get the quotient value is 14.
Question 14.
Answer: The quotient value is 21 R 7.
Explanation: Given that, the values are 868 and 41.
Now we will find the quotient value.
After dividing, to get the quotient value is 21 R 7.
Question 15.
Answer: The quotient value is 19.
Explanation: Given that, the values are 646 and 34.
Now we will find the quotient value.
The below is the division process,
After division, to get the quotient value is 19.
Question 16.
Answer: The quotient value is 58 R 9.
Explanation: Given that, the values are 879 and 15.
Now, we will find the quotient value.
After division, to get the quotient value is 58 R 9.
Question 17.
Answer: The quotient value is 32 R 9.
Explanation: Given that, the values are 329 and 10.
Now we will find the quotient value.
The division process is,
After dividing, to get the quotient value is 32 R 9.
Question 18.
Answer: The given values quotient is 8.
Explanation: Given that, the values are 784 and 98.
Now, we need to find the quotient value.
After dividing, to get the quotient value is 8.
Question 19.
Answer: The quotient value is 25.
Explanation: Given that, the values are 975 and 39.
Now, we will find the quotient value.
After division, the quotient value is 25.
Question 20.
Answer: The quotient value is 14 R 2.
Explanation: Given that, the values are 660 and 47.
Now we will find the quotient value.
The division process is,
After division, to get the quotient value is 14 R 2.
Fluency Practice
Divide.
Question 1.
Answer: The quotient value is 2516.
Explanation: Given that, the values are 32708 and 13.
Now we will find the quotient value.
After division to get the quotient value is 2516.
Question 2.
Answer: The quotient value is 1078.
Explanation: Given that, the values are 81928 and 76.
Now we will find the quotient value.
After division the quotient value is 1078.
Question 3.
Answer: The quotient value is 1218 R 3.
Explanation: Given that, the values are 65775 and 54.
Now we will find the quotient value.
After division the quotient value is 1218 R 3.
Question 4.
Answer: The quotient value is 875 R 3.
Explanation: Given that, the values are 72628 and 83.
Now we will find the quotient value.
After division the quotient value is 875 R 3.
Question 5.
Answer: The quotient value is 995 R 5.
Explanation: Given that, the values are 22890 and 23.
Now, we need to find the quotient value.
The division of the given values is,
After division the quotient value is 995 R 5.
Question 6.
Answer: The quotient value is 1007.
Explanation: Given that, the values are 61427 and 61.
Now we will find the quotient value.
So, the given values division process is,
After division the quotient value is 1007.
Question 7.
Answer: The quotient value is 732 R 1.
Explanation: Given that, the values are 65881 and 90.
Now, we need to find the quotient value.
The below is the division process,
After division, to get the quotient value is 732 R 1.
Question 8.
Answer: The quotient value is 2346.
Explanation: Given that, the values are 89148 and 38.
Now, we will find the quotient value.
The division process is,
After division the quotient value is 2346.
Question 9.
Answer: The quotient value is 6164.
Explanation: Given that, the values are 92460 and 15.
Now, we will find the quotient value.
After division to get the quotient value is 6164.
Question 10.
Answer: The quotient value is 651 R 5.
Explanation: Given that, the values are 27998 and 43.
Now we will find the quotient value.
After division the quotient value is 651 R 5.
Question 11.
Answer: The quotient value is 2287 R 3.
Explanation: Given that, the values are 61752 and 27.
Now we will find the quotient value.
After division the quotient value is 2287 R 3.
Question 12.
Answer: The quotient value is 578.
Explanation: Given that, the values are 50286 and 87.
Now, we will find the quotient value.
The division process is,
After division to get the quotient value is 578.
Question 13.
Answer: The quotient value is 75.
Explanation: Given that, the values are 16200 and 216.
Now, we will find the quotient value.
So, the division process is,
After dividing to get the quotient value is 75.
Question 14.
Answer: The quotient value is 108.
Explanation: Given that, the values are 60156 and 557.
Now we will find the quotient value.
After dividing 60156 by 557. To get the quotient value is 108.
Question 15.
Answer: The quotient value is 254 R 7.
Explanation: Given that, the values are 80779 and 318.
Now, we will find the quotient value.
The division process is,
After division to get the quotient value is 254(7/318) i.e., 254 R 7.
Question 16.
Answer: The quotient value is 104 R 6.
Explanation: Given that, the values are 89550 and 861.
Now we will find the quotient value.
The division process is,
After division the quotient value is 104 (6/861) i.e., 104 R 6.
Question 17.
Answer: The quotient value is 224
Explanation: Given that, the values are 88704 and 396.
Now we will find the quotient value.
After division to get the quotient value is 224.
Question 18.
Answer: The quotient value is 375 R 14
Explanation: Given that, the values are 82889 and 221.
Now we will find the quotient value.
After division the quotient value is 375 (14/221) i.e., 375 R 14.
Question 19.
Answer: The quotient value is 98 R 27.
Explanation: Given that, the values are 55103 and 562.
Now we will find the quotient value.
After division the quotient value is 98 (27/562) i.e., 98 R 27.
Question 20.
Answer: The quotient value is 102
Explanation: Given that, the values are 92004 and 902.
Now we will find the quotient value.
After division the quotient value is 102.