All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 5 Lesson 5 Solve Multi-Step Word Problems will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 5 Lesson 5 Solve Multi-Step Word Problems
Math in My World
Example 1
Francis earns $8 each week walking dogs. She spends $3 each week and saves the rest. There are 52 weeks in a year. How much will she have saved at the end of the year?
You need to find ($8 – $3) × 52. The operations that are needed for this problem are subtraction and multiplication.
So, Francis will have saved $________.
Check
$_____ is close to the estimate of $250. So, the answer is correct.
Answer: So, Francis will have saved $260.
$260 is close to the estimate of $250. So, the answer is correct.
Explanation:
Given that,
Francis earns $8 each week walking dogs.
She spends $3 each week and saves the rest.
There are 52 weeks in a year.
Now, we will find out how much will she have saved at the end of the year.
So, the values are 8-3 = 5.
multiply 5 and 52. We get the actual value.
But the estimated value is 52 is rounded off to 50.
Then 5 x 50 = 250.
The actual value is,
Hence, Francis will have saved $260.
$260 is close to the estimate of $250. So, the answer is correct.
Example 2
Coach Murphy bought three boxes of trophies. Each box has 45 soccer trophies. He also bought 15 tennis trophies and some golf trophies. There are a total of 170 trophies. Write an equation to describe the number of trophies that Coach Murphy bought. How many golf trophies did Coach Murphy buy? Write an equation. Solve for the unknown quantity.
So, Coach Murphy bought ___ golf trophies.
Answer: Coach Murphy bought 20 golf trophies.
Explanation:
Given that,
Coach Murphy bought three boxes of trophies.
Each box has 45 soccer trophies. He also bought 15 tennis trophies and some golf trophies.
There are a total of 170 trophies.
Now, we will write an equation describing the number of trophies that Coach Murphy bought.
First, find out how many golf trophies did Coach Murphy buy and solve for the unknown quantity.
So, the values are,
Now, add the values.
Now, we will find the unknown quantity.
So, the value of the unknown quantity g is 20.
Hence, Coach Murphy bought 20 golf trophies.
Talk Math
Why are variables used?
Answer:
Variables are used to store information to be referenced and manipulated in a computer program. They also provide a way of labeling data with a descriptive name, so our programs can be understood more clearly by the reader and ourselves. It is helpful to think of variables as containers that hold information.
Guided Practice
Question 1.
Karrie has 20 bags of prizes. Each bag has 4 prizes. She also has a red bag with 13 prizes and a blue bag with the rest of the prizes. She has a total of 100 prizes. How many prizes are in the blue bag? Write an equation. Use a variable for the unknown number.
Answer: 9 prizes are in the blue bag.
Explanation: As given in the equation,
Karrie has 20 bags of prizes. Each bag has 4 prizes.
She also has a red bag with 13 prizes and a blue bag with the rest of the prizes.
She has a total of 100 prizes.
Now, we need to find out how many prizes are in the blue bag and write an equation using a variable for the unknown number.
So, the equation is,
(20 x 4) + 13 + b =100
80 + 13 + b = 100
93 + b = 100
b = 100 -93
b =9
Hence, in a blue bag, 9 prizes will be there.
Independent Practice
Algebra Write an equation for each problem. Solve.
Question 2.
Each small dog at doggy daycare weighs 35 pounds. Each large dog weighs 60 pounds. There are 4 small dogs and 6 large dogs. How much do the dogs weigh altogether?
Answer:
The weight of the altogether dogs is 500.
Explanation:
As given in the question, the data is,
Each small dog at doggy daycare weighs 35 pounds.
Each large dog weighs 60 pounds.
There are 4 small dogs and 6 large dogs.
Now, we will find out how much the dogs weigh altogether.
So, the weight of small dogs is 4 x 35,
Next, the weight of large dogs is,
6 x 60 = 360.
The total weight of the dogs is,
140 + 360 = 500.
Hence, the dogs weigh altogether is 500.
Question 3.
Suzie has track practice for 1 hour on Tuesday and 2 hours on Thursday. How many hours does Suzie go to track practice in 15 weeks?
Answer: 45 hours Suzie goes to track practice in 15 weeks.
Explanation:
Given that,
Suzie has track practice for 1 hour on Tuesday and 2 hours on Thursday.
Now, we will determine how many hours Suzie goes to track practice in 15 weeks.
Based on the given information, in a week Suzie practices 3 hours.
So, for 15 weeks, 15 x 3 is
Hence, Suzie goes to track practice in 15 weeks is 45 hours.
Algebra Write an equation for each problem. Use a variable for the unknown number. Solve.
Question 4.
Warren, Lisa, and Tina went to the carnival. The table shows the number of points Warren won at each carnival game.
Lisa won the same number of points as Warren. Warren, Lisa, and Tina won a total of 225 points. How many points did Tina win?
Answer: Tina wins 125 points.
Explanation:
Given that,
Warren, Lisa, and Tina went to the carnival.
Lisa won the same number of points as Warren.
Warren, Lisa, and Tina won a total of 225 points.
Now, we need to find out how many points Tina win.
So, Warren won the points is,
24 + 16 + 10 = 50.
Lisa and Warren won the same points.
I.e., 50 + 50 = 100.
Now, we will find Tina’s points.
Then 225 – 100 = 125.
Therefore, Tina won 125 points.
Question 5.
Mark bought four hats that each cost $8. He also bought a shirt that cost $14 and a pair of jeans. He spent a total of $68. How much did the jeans cost?
Answer: The jeans cost $ 46.
Explanation:
Given that,
Mark bought four hats that each cost $8.
He also bought a shirt that cost $14 and a pair of jeans.
He spent a total of $68.
Now, we will find out how much the jeans cost.
So, the total value of hats and shirts is
14 + 8 = 22.
Now, we will find the cost of jeans.
i.e., 68 – 22 = 46.
Hence, the cost of the jeans is $46.
Problem Solving
Use a number cube to complete each number puzzle.
Question 6.
Mathematical PRACTICE 1 Keep Trying Roll a number cube four times. The numbers rolled are ___, ___, _____, and ____.
Write the numbers in the boxes below. Use each number once. Try to create the greatest number possible.
Answer: The numbers rolled are 6, 5, 4, and 1.
Explanation:
Given a cube with the numbers 1, 2, 3, 4, 5, and 6.
We can roll a cube four times.
Using these numbers, we can find the greatest number.
So, the numbers rolled are 6, 5, 4, and 1.
The above-rolled numbers are substituted in the given expression, and we get
(6 x 5 )+4-1 = 30 + 3 = 33.
Therefore, the greatest number is 33.
Question 7.
Roll a number cube four times. The numbers rolled are: ___, ___, ____, and _____
Write the numbers in the boxes below. Use each number once. Try to create the greatest number possible.
Answer: The numbers rolled are 12, 11, 10, and 7.
Explanation:
Given a cube with the numbers 7, 8, 9, 10, 11, and 12.
We can roll a cube four times.
Using these numbers, we can find the greatest number.
So, the numbers rolled are 10, 12, 11, and 7.
The above-rolled numbers are substituted in the given expression, and we get
10 + (12 x 11) – 7 = 10 + 132 -7 = 142 – 7 = 135.
Therefore, the greatest number is 135.
HOT Problems
Question 8.
Mathematical PRACTICE 1 Make Sense of Problems A bus has 15 rows of seats. Each row has 4 seats. At the first stop, 25 people get on the bus. At the second stop, 3 people get off the bus, and 12 people get on the bus. How many empty seats are there after the second stop?
Answer: 32 empty seats are there after the second stop
Explanation:
As given that,
A bus has 15 rows of seats.
Each row has 4 seats.
At the first stop, 25 people get on the bus.
At the second stop, 3 people get off the bus, and 12 people get on the bus.
Now, we will find out how many empty seats are there after the second stop.
So, the values are 15 and 4
i.e., 15 x 4 = 60
The total number of seats is 60.
Now, we will find the final empty seats.
So, the first and second stop-off people are 25 and 3.
then 60 – 28 = 32.
Therefore, 32 empty seats are there after the second stop.
Question 9.
? Building on the Essential Question How can I use equations to model real-world problems?
Answer:
I can write an equation to model a real-world problem is often easier when you take the information given in the problem and express it in verbal form by using a few keywords. This is very similar to translating verbal phrases into variable expressions.
McGraw Hill My Math Grade 4 Chapter 5 Lesson 5 My Homework Answer Key
Practice
Question 1.
Gina works at a diner. She earns $6 each hour plus tips. In one week, she worked 37 hours a week and earned $43 in tips. How much did she make altogether? Write an equation. Use a variable for the unknown. Solve.
Answer: The equation is, 6x +43 = y.
The total money earned by Gina in a week is $265.
Explanation:
Given that,
Gina works at a diner.
She earns $6 each hour plus tips.
In one week, she worked 37 hours a week and earned $43 in tips.
Now, we will find out how much did she make altogether with the equation.
So, the equation is,
6x +43 = y
Let ‘x’ be the number of hours she worked.
i.e., (6 x 37) + 43 = y
222 + 43 = y
265 = y.
Hence, she earned altogether money is $265.
Problem Solving
Write an equation for each problem. Use a variable for the unknown number. Solve.
Question 2.
Mathematical PRACTICE 2 Use Number Sense It costs $45 to rent a car each day. There is also a fee of $12. How much does it cost to rent a car for 5 days, including the fee?
Answer: The equation is y = 12 + 45x
The total cost for 5 days is $237.
Explanation:
Given that,
It costs $45 to rent a car each day.
There is also a fee of $12.
Now, we will find out how much it costs to rent a car for 5 days, including the fee.
Let ‘x’ be the number of hours i.e., 45x
The total cost for x days is 12+45x
The ‘y’ will be the total cost.
The equation is y = 12 + 45x
y = 12 + 45 (5)
y = 12 + 225
y = 237.
Hence, the total cost for 5 days is $237.
Question 3.
A climbing gym charges $10 to climb each day. A pair of climbing shoes costs $84. It costs $169 to buy 6 days of climbing, one pair of climbing shoes, and one harness. How much does a harness cost?
Answer:
The equation is 6x + y + z = 169.
A harness cost is $25.
Explanation:
Given that,
The charge for 1 day of climbing is represented as ‘x’, x = $10.
The price of 1 pair of climbing shoes is represented as ‘y’, y = $84.
Let the price of 1 harness be represented by z.
The total cost is $169.
Now, we will write the equation.
The equation is,
6x + y + z = 169.
Substitute the values to get,
6(10) + 84 + z= 169.
60 + 84 + z = 169.
144 + z = 169.
169 – 144 = z
z = 25.
Therefore, a harness cost is $25.
Question 4.
A travel agency charges $64 for each bus ticket and $82 for each train ticket. How much does it cost to buy 3 bus tickets and 4 train tickets?
Answer: The equation is 64x + 82y = z.
The total cost for 3 bus tickets and 4 train tickets is $520.
Explanation:
Given that,
A travel agency charges $64 for each bus ticket and $82 for each train ticket.
Now, we will find out how much it costs to buy 3 bus tickets and 4 train tickets using the equation.
So, the equation is,
Let ‘x’ be the number of bus tickets i.e., 64x.
Let ‘y’ be the number of train tickets i.e., 82y.
The total cost is z.
Hence, the equation is 64x + 82y = z.
Now, substitute x and y values we get the z value.
(64 x 3) + ( 82 x 4) = z
192+ 328 = z
520 = z.
There, the cost of 3 bus tickets and 4 train tickets is $520.
Vocabulary Check
Question 5.
Label each part of the equation. Write operation or variable.
Answer: Each part of the given equation is,
Test Practice
Question 6.
There are three shelves. Each shelf has 28 books. There is also a stack of some more books. There are a total of 85 books. Which equation represents this situation?
A. (3 × 28) + b = 85
B. (3 + 28) × b = 85
C. (3 × 28) + 85 = b
D. (3 + 28) × 85 = b
Answer: Option A
Explanation:
Given that,
There are three shelves.
Each shelf has 28 books.
There is also a stack of some more books.
There are a total of 85 books.
Now, we will write the equation with represents this situation.
So, the equation is,
3 x 28 ( Three selves, each shelf has 28 books)
Some more books will be there. Let it be ‘b’.
i.e., (3 x 28) + b
The total number of books is 85.
Therefore, the equation is (3 x 28) + b = 85.