All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 8 Lesson 4 Problem-Solving Investigation: Guess, Check, and Revise will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 8 Lesson 4 Problem-Solving Investigation: Guess, Check, and Revise
1. Understand
What facts do you know?
- Bactrian camels have two humps and Dromedary camels have one hump.
- There are 20 camels with 28 humps.
What do you need to find?
- How many camels of each type are there?
2. Plan
I will guess, check, and revise to solve the problem.
3. Solve
So, there are 8 Bactrian camels and 12 Dromedary camels.
4 Check
Is my answer reasonable?
10 + 10 = 20 camels and 8 +12 = 28 humps
Practice the Strategy
Conner spent $66 on rookie cards and Hall of Famer cards. How many of each type of card did he buy?
1. Understand
What facts do you know?
Conner spent $66 on rookie cards and Hall of Famer cards
We know that rookie cards are four for six
Hall of Famer cards two for nine
What do you need to find’
How many of each type of card did he buy
2. Plan
I will guess, check, and revise to solve the problem.
3. Solve
Therefore we calculate:
5 x 6 + 4 x 9 = 30+36 = 66
5 x 4 = 20 rookie cards
4 x 2 = 8 Hall of Famer cards
Conner buyed 20 rookie cards and 8 Hall of Famer cards
4. Check
Is my answer reasonable?
30 + 36 = 66 and he spent total $66
Apply the Strategy
Guess, check, and revise to solve each problem.
Question 1.
Bike path A is 4 miles long. Bike path B is 7 miles long. If April biked a total of 37 miles, how many times did she bike each path?
Answer:
Bike path A is 9.3 times so 9
Bike path B is 5.3 times
Explanation:
37 divided by 7 = 5.2 so 5
37 divided by 4 = 9.2 so 9
So bike path of A 9 times and bike path of B 5 times
Question 2.
Ruben sees 14 wheels on a total of 6 bicycles and tricycles. How many bicycles and tricycles are there?
Answer:
4 bicycles
2 tricycles
Explanation:
Total no of wheels = 14
A tricycle has 1 wheel extra compared to bicycle.
So, if all the 6 were bicycles, number of wheels would have been 6 x 2 = 12
Now 12 is 2 less than actual no of wheels14.
These extra wheels are for each tricycle. So the no of tricycles are 2
So, 2 x 3 = 6 and 4 x 2 = 8, 6 + 8 = 14 wheels
Question 3.
A teacher is having three students take care of 28 goldfish during the summer. He gave some of them to Alaina. Then he gave twice as many to Miguel. He gave twice as many to Kira as he gave to Miguel. How many fish did each student get?
Answer:
Alaina got 4, Miguel got 2(4) = 8 while Kira got 2(8) = 16
Explanation:
let the number he gave to Alaina be x.
Now we know he gave twice as many to Miguel. Amount received by Miguel is 2x.
He gave Kira 2 times what he gave Miguel, that is 2 x 2 = 4x
Addition of all these equals 28. we now get x
4x + 2x +x = 28
7x = 28
x = \(\frac{28}{7}\)
x = 4
Alaina got 4, Miguel got 2(4) = 8 while Kira got 2(8) = 16
Question 4.
Ticket prices for a science museum are $18 for adults and $12 for students. If $162 is collected from a group of 12 people, how many adults and students are in the group?
Answer:
3 adults and 9 students
Explanation:
x = number of adults and y = number of students
x + y = 12
18x + 12y = 162
You can simplify second equation by dividing by six
3x + 2y = 27
rearrange first equation y = 12-x.
Plug y into simplified second equation:
3x + 2(12-x)= 27
3x -2x+24 = 27
x = 3
y = 12-x so 12 – 3 = 9
3 adults and 9 students
Question 5.
Mathematical PRACTICE 1 Keep Trying Jerome bought 2 postcards and received $1.35 in change in quarters and dimes. If he got 6 coins back, how many of each coin did he get?
Answer:
5 quarters and 1 dime
Explanation:
Let q be quarters and d be dime
q+d= 6 subtract q from both sides:
q= 6-d
0.25q+0.10d= 1.35
0.25(6-d)+0.10d= 1.35
1.50-0.25d+0.10d= 1.35
-0.15d= -0.15
d= -0.15/-0.15
d= 1 He got 1 dime and
6-1= 5 quarters back
Check:
5 x 0.25= 1.25
1 x 0.10= 0.10
Total: 1.35 We have the correct answer
Question 6.
A tour director collected $258 for 13 tour packages. Tour package A costs $18 and tour package B costs $22. How many of each tour package were sold?
Answer:
6 tour packages A and 7 tour package B were sold.
Explanation:
a + b = 13
22a + 18b = 258
a = 13-b
22 x (13-b) + 18b = 258
286 – 22b + 18b = 258
-4b = 258-286
-4b = -28
b = (-28) : (-8) = 7
a = 13 – 7 = 6
Review the Strategies
Use any strategy to solve each problem.
- Guess, check, and revise.
- Work backward.
- Determine an estimate or exact answer.
- Make a table.
Question 7.
The sum of two numbers is 30. Their product is 176. What are the two numbers?
Answer:
8 and 22
Explanation:
a + b = 30
a x b = 176
putting values of a from 1 in 2
(30 – b) b = 176
30b – b^2 = 176
b^2 – 30 b + 176 = 0
b^2 – 22b -8b + 176 =0
b( b – 22) – 8(b-22) = 0
(b-22) (b – 8)= 0
b – 22 = 0
b = 22
b – 8 = 0
b = 8
so for b= 22 , a = 30-b = 8
Question 8.
Mathematical PRACTICE 1 Make a Plan Howard downloaded 6 more songs than Erin. Lee downloaded 3 more than Howard. Lee downloaded 16 songs. How many songs did Erin download?
Answer:
Erin downloaded 7 songs
Explanation:
If lee downloaded 3 more than Howard(16 total songs) ,that means Howard downloaded 13 songs (total)
If Howard downloaded 13 songs, he downloaded 6 more than Erin.
Therefore, you would subtract 6 from 13 to get 7
So, Erin downloaded 7 songs
Question 9.
Algebra Work backward to find the value of the variable in the equation below.
d – 4 = 23
Answer:
27
Explanation:
d – 4 = 23
In order to isolate the variable or get the variable by itself, you need to get rid of constants around it or the numbers without a variable.
In order to do that for this equation , you’ll need to do the inverse of subtracting 4, which would be adding four to both sides. adding 4 to positive 23 will give you the answer of 27
d = 27
Therefore , the variable d equals 27
Question 10.
A bakery can make 175 pastries each day. The bakery has been sold out for 3 days in a row. Determine if an estimate or exact answer is needed. Then determine how many pastries were sold during the 3 days.
Answer:
525 pastries were sold in 3 days.
Explanation:
An exact amount of 525 pastries because the bakery can only make a maximum of 175 daily so there would be no estimate since you have the exact number.
Question 11.
Charlotte bought packages of hot dogs for $4 each. Each package contains 8 hot dogs. If she spent $16 on hot dogs, how many hot dogs did she buy?
Answer:
Charlotte bought 32 hot dogs for $16 a pack
Explanation:
If she spent $16 on hot dogs $4 each
\(\frac{16}{4}\) = 4
Then , Each package contains 8 hot dogs
So, 8 x 4 = 32
Charlotte bought 32 hot dogs for $16 a pack
Question 12.
Mr. Thompson took his 5 children to the bowling alley. The cost for children 12 and older ¡s $3.50. The cost for children under 12 is $2.25. He spends a total of $16.25. How many of his children are 12 and older?
Answer:
4 children over 12 and 1 under 12
Explanation:
The cost for children 12 and older is $3.50.
The cost for children under 12 is $2.25.
He spends a total of $16.25.
4 are 12yrs that is 3.50 x 4 = $14.00
1 under 12 that is 2.25x 1 = $2.25
total $16.25
McGraw Hill My Math Grade 5 Chapter 4 Lesson 4 My Homework Answer Key
Problem Solving
Guess, check, and revise to solve each problem.
Question 1.
A cabin has room for 7 campers and 2 counselors. How many cabins are needed for a total of 49 campers and 14 counselors?
Answer:
7 cabins are needed.
Explanation:
As it turns out, 49 campers divided by 7campers per cabin equals 7 cabins, and 14 counselors divided by 2 counselors per cabin equals 7 cabins.
Question 2.
Marcus is selling lemonade and peanuts. Each cup of lemonade costs $0.75, and each bag of peanuts costs $0.35. On Saturday, Marcus sold 5 more cups of lemonade than bags of peanuts. He earned $7.05. How many cups of lemonade did Marcus sell on Saturday?
Answer:
Marcus sold 8 cups of lemonade and 3 bags of peanuts.
Explanation:
Marcus is selling lemonade and peanuts.
Let X = lemonade
Let Y = peanuts
On Saturday, Marcus sold 5 more cups of lemonade than bags of peanuts
So, X = Y + 5 and he earned 7.05
Forming the equation.
[(Y+5) x 0.75] + (Y x 0.35) = 7.05
0.75Y + 3.75 + 0.35Y = 7.05
1.1Y = 7.05 – 3.75
1.1Y = 3.3
Y = 3
So the number of cups of lemonade is Y + 5 = 3 + 5 = 8
So there are 8 cups.
Question 3.
Mathematical PRACTICE 1 Keep Trying In a recent year, a letter to Europe from the United States costs $0.94 to mail. A letter mailed within the United States costs $0.44. Nancy mailed 5 letters for $3.70, some to Europe and some to the United States. How many letters did she send to Europe?
Answer:
she send 3 letters to Europe and 2 within the USA
Explanation:
There are two unknowns: how many letters went to Europe (x) and how many letters went to US (y)
We know the total number of letters mailed was 5, therefore
x + y = 5
We also know how much was spent per type of letter and in total, therefore…
0.94x + 0.44y = 3.70
Solving the first equation in terms of y, we get
y = -x + 5
By substituting that information into the second equation, we see
0.94x + 0.44(-x + 5) = 3.70
Distributing we find…
0.94x + -0.44x + 2.20= 3.70
Combining like terms….
0.50x + 2.20 = 3.70
Using the subtraction property of equality we find
0.50x = 1.50
Division property of equality
x = 3
Question 4.
Alma counts 26 legs in a barnyard with horses and chickens. If there are 8 animals, how many are horses?
Answer:
5 horses
Explanation:
You need to make 2 equations:
h + c = 8 (horses + chickens = 8 animals)
4h + 2c = 26 (4 legs for each horse, plus 2 legs for each chicken, = 26 total legs.
Rearrange the top equation so it’s c = 8 – h, and plug in “8 – h” in place of c in the second equation:
4h + 2(8 – h) = 26, then distribute and combine terms to get
4h + 16 – 2h = 26, which becomes
2h = 10
h = 5, so there are 5 horses; therefore there must be 3 chickens.
5 horses = 20 horse legs; 3 chickens = 6 chicken legs; total = 26 legs.
Question 5.
A volleyball league organizer collected $2,040 for both divisions of volleyball teams. The Blue division costs $160 per team and the Red division costs $180 per team. How many teams will play in each division?
Answer:
Six teams will play in each division.
Explanation:
If we are to assume that an equal amount of teams will play in each division:
Let x = the number of teams in each division
Then create the proper equation and solve for x.
160x + 180x = 2040 (next add the coefficients)
340x = 2040 (and divide both sides by the coefficient 340)
x = 6
Six teams will play in each division.