# McGraw Hill My Math Grade 5 Chapter 1 Lesson 9 Answer Key Problem-Solving Investigation: Use the Four-Step Plan

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 1 Lesson 9 Problem-Solving Investigation: Use the Four-Step Plan will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 1 Lesson 9 Problem-Solving Investigation: Use the Four-Step Plan

1. Understand

What facts do you know?

A total of ___ was spent. ___ packages of the smallest-grain sandpaper were purchased.

What do you need to find?
the number of packages of the largest grain sandpaper he bought

2. Plan
To solve this problem, I can work backwards.

3. Solve
The smallest size is ___ centimeter. Victor spent 2 × ___ or ____.
Subtract to find the remaining amount spent: $61 – ___ = ____ The largest size is 0.011 centimeter. Each package costs$7.
Victor bought $21 ÷$7, or ___ packages of the largest grain sandpaper.

4. Check

1. Understand

What facts do you know?
________________
________________

What do you need to find?
________________

2. Plan
________________
________________

3. Solve

4. Check
________________

Apply the Strategy

Solve each problem using the four-step plan.

Question 1.
The table shows the number of ounces of buffer Marti used in different recipes. She has 6 ounces of butter left. How many ounces of butter did she have at the beginning?

The Ounces of butter used for Pie = 4
The Ounces of butter used for Cookies = 8
The Ounces of butter used for Pasta = 6
The Ounces of butter she had left with = 6
The ounces of butter did she have at the beginning = X
Now add all the butter used for recipes and the butter she had left with.
X = (4 + 8 + 6) + 6
X = 24
Therefore, she had 24 ounces of butter at the beginning.

Question 2.
At the end of their 3-day vacation, the Palmers travelled a total of 530 miles. On the third day, they drove 75 miles. On the second day, they drove 320 miles. How many miles did they drive the first day?

The total number of miles they travelled = 530
The number of miles they drove on the third day = 75
The number of miles they drove on the second day = 320
The number of miles they drove on the first day = X
X = total miles – number of miles they drove on the second and third day
X = 530 – 320 + 75
X = 530 – 395
X = 135
Therefore, they drove 135 miles on the first day.

Question 3.
Mathematical PRACTICE Keep Trying You divide a number by 3, add 6, and then subtract 7. The result ¡s 4. What is the number?
Let the number be ‘n’
Now divide the number(n) by 3.
n/3 + 6 – 7 = 4
Now solve the equation.
n/3 – 1 = 4
n – 3/3 = 4
n – 3 = 12
n = 12 + 3
n = 15
Now substitute n value in the equation.
15 – 3 = 12
12 = 12
LHS = RHS

Question 4.
Mr Toshio lent out 11 rulers at the beginning of class, collected 4 rulers in the middle of class, and gave out 7 at the end of class. He had 18 at the end of the day. How many rulers did he start with?
The number of rulers Mr Toshio lent out at the beginning of the class is 11
The number of rulers Mr Toshio collected in the middle of class = 4
The number of rulers he gave out at the end of the class = 7
The number of rulers he had at the end of the day was 18
The number of rulers he had at the beginning = X
X = (11 – 4) + 18 + 7
X = 7 + 18 + 7
X = 32
Therefore, he started with 32 rulers.

Question 5.
The Math Club ¡s selling gift wraps for a fundraiser. They sold all 45 rolls of solid wrapping paper at
$4 each and rolls of patterned wrapping paper at$5 each. If they made $265, how many rolls of patterned wrapping paper did they sell? Answer: The cost of each solid wrapping paper is$4
The cost of each patterned wrapping paper is $5 The solid wrapping paper = 45 x 4 = 180 If they made$265, then how many patterned wrapping paper rolls did they sell. Let it be X.
265 – 180 = 85
X = 85/5
X = 17
Therefore, they sell 17 patterned wrapping rolls.

Review the Strategies

Use any strategy to solve each problem.

• Use the four-step plan.
• Make a table.
• Act it out.

Question 6.
Mathematical PRACTICE Make a Plan Ming-Li spent $15 at the movies. She then earned$30 babysitting. She spent $12 at the bookstore. She now has$18 left. How much money did Ming-Li have to begin with?
The amount she spent on movies = $15 The amount she earned on babysitting =$30
The amount she spent at the bookstore = $12 The amount she has left =$18
The amount she has to begin with = X
X – 15 + 30 – 12 = 18
X – 15 + 18 = 18
After solving the equation, we get
18 gets cancelled.
X – 15 = 0
X = 15
Therefore, the money she begin with $15. Question 7. Mr. Jenkins bought payers for some landscaping projects. He used 120 for a small patio, 86 for the border of a flower bed, and 70 for a wall. He has 24 payers left. How many payers did Mr. Jenkins buy? Answer: The number of payers he used for the small patio = 120 The number of payers he used for the flower bed = 86 The number of payers he used for the wall = 70 The number of payers left = 24 The number of payers he buys = X X = 120 + 86 + 70 + 24 X = 300 Therefore, he bought 300 payers. Question 8. The table shows the number of candy bars the cheerleaders sold each week. They have 9 candy bars left. How many candy bars did they have to sell to begin with? Answer: The candy bars they sold in the first week = 117 The candy bars they sold in the second week = 130 The candy bars they sold in the third week = 83 the number of candy bars left = 9 The number of candy bars they have to sell, to begin with, = X X = 110 + 130 + 83 + 9 X = 339 Therefore, the candy bars, they have to sell, to begin with, are 339. Question 9. You multiply a number by 3, subtract 6 and then add 2. The result is 20. What is the number? Answer: Let the number be n 3n – 6 + 2 = 20 Solve the equation. 3n – 4 = 20 3n = 20 + 4 3n = 24 n = 24/3 n = 8 Question 10. Dimitrius returned 5 library books last week, returned 3 books this week, and then checked out 8 more books. He now has 12 library books. How many books did he have before last week? Answer: The above-given information: The number of books he returned last week = 5 The number of books he returned this week = 3 The number of books he checked out = 8 The number of library books he has = 12 The number of books he has before last week = x 5 + 3 + 8 – x = 12 16 – x = 12 – x = 12 – 16 -x = -4 x = 4 Therefore, he has 4 books before last week. ### McGraw Hill My Math Grade 5 Chapter 1 Lesson 9 My Homework Answer Key Problem Solving Solve each problem using the four-step plan. Question 1. The table shows the number of vehicles washed at a car wash fundraiser over the weekend. If there were a total of 94 vehicles, how many were washed on Saturday? Answer: The above-given information: The number of vehicles on Friday = 27 The number of vehicles on Sunday = 34 The number of vehicles on Saturday = x The total number of vehicles = 94 x = 94 – (34 + 27) x = 94 – 61 x = 33 Therefore, the vehicles washed on Saturday is 33. Question 2. The volleyball team sold 16 items on the first day of a bake sale, 28 items on the second day, and 12 items on the last day. There were 4 items left that had not been purchased. How many total items were for sale at the bake sale? Answer: The number of items sold by the Volleyball team on the first day = 16 The number of items sold by the Volleyball team on the second day = 28 The number of items sold by the Volleyball team on the third day = 12 The number of items left that are not purchased = 4 The number of total items = x x = add all the items to get the total x = 16 + 28 + 12 + 4 x = 60 Therefore, the total items are 60. Question 3. Ricardo lost 6 golf balls while playing yesterday. He bought a box of 12 golf balls, then lost 4 on the course today. He now has 18 golf balls. How many golf balls did Ricardo have to begin with? Answer: The above-given information: The number of golf balls he lost yesterday = 6 The number of balls he bought today = 12 The number of balls he lost today = 4 The number of balls he has present = 18 The number of golf balls he has to begin with = x x = 12 + 18 – 6 – 4 x = 12 + 18 – 10 x = 30 – 10 x = 20 Therefore, he has to begin with 20 golf balls. Question 4. The distance between Cincinnati, Ohio, and Charlotte, North Carolina, is about 336 miles. The distance between Cincinnati and Chicago, Illinois, is about 247 miles. If Perry drove from Charlotte to Chicago by way of Cincinnati, find the distance he drove. Answer: Cincinnati, Ohio, and Charlotte, North Carolina all are considered as x1 Cincinnati and Chicago, Illinois are considered as x2 The distance between the cities(x1) = 336 The distance between the cities(x2) = 247 The distance we need to find out for Charlotte to Chicago by way of Cincinnati = D D = 336 – 247 D = 89 Therefore, the distance he dove is 89 miles. Question 5. Mathematical PRACTICE Plan Your Solution Adison earned$25 mowing her neighbor’s lawn. Then she loaned her friend $18, and got$50 from her grandmother for her birthday. She now has $86. How much money did Adison have to begin with? Answer: Let x be the beginning amount of money The amount earned by Addison by mowing her neighbour’s lawn =$25
The amount she loaned from her friend = $18 The amount she got a birthday gift from her grandmother =$50
the amount she has present = $86 the expression to solve this question is x + 25 – 18 + 50 = 86 x + 75 – 18 = 86 x + 57 = 86 x = 86 – 57 x = 29 Therefore, the beginning amount of money is$29

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