All the solutions provided in McGraw Hill My Math Grade 3 Answer Key PDF Chapter 9 Lesson 8 Solve Two-Step Word Problems will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 3 Answer Key Chapter 9 Lesson 8 Solve Two-Step Word Problems
Sometimes in order to solve a problem you need to do more than one step or use more than one operation.
Example 1
Gustavo bought some tools at the hardware store. He bought five tools for $6 each and one tool for $7. How much did he spend altogether on tools?
Write an equation with a letter for the unknown. Then solve.
Helpful Hint
When there are no parentheses, multiply and divide first in order, from left to right. Then add and subtract in order, from left to right.
So, 5 × $6 + $7 = $____________. The unknown is $ ____________.
Gustavo spent $____________ on tools.
Check: Use mental math to check your answer for reasonableness.
Gustavo had $37 and spent $7. $37 – $7 = $ ______________
Since $30 ÷ 5 tools = $_____________ each, the answer is reasonable.
Answer: Gustavo spent $37 on tools
Explanation:
Checking,
Gustavo had $37 and spent $7.
$37 – $7 = $30
Since $30 ÷ 5 tools = $6
So, the answer is reasonable.
Example 2
Orion has 48 comic books. He keeps 8 for himself and divides the rest equally among his friends. If each friend gets 8 comic books, to how many friends did he give comic books?
Write an equation with a letter for the unknown. Then solve.
So, (48 – 8) ÷ _____________ = 8. The unknown is _____________.
Orion gave ___________ of his friends comic books.
Check: Use estimation to check your answer for reasonableness.
The estimate 4 is close to the actual number of 5. The answer is reasonable.
Talk Math
How could you check an equation for reasonableness?
Answer: Rounding numbers, making numbers compatible, properties of operations are some strategies that are used to check the reasonableness of answers.
Explanation:
For instance, in a division problem like 424 ÷ 4 − 10, we can check is our answer is reasonable or not, by estimating an approximate answer or by using the division formula.
We can round down 424 to the nearest hundreds, to estimate the answer.
That will be 400.
Guided Practice
Write an equation with a letter for the unknown. Then solve. Check for reasonableness.
Question 1.
A city bus had 14 passengers. At a stop, 5 people got off and 8 people got on. How many people are on the bus now?
Answer: There are 17 people on the bus.
Explanation:
Given, A city bus had 14 passengers.
At a stop, 5 people got off and 8 people got on.
Let the unknown be y ,
The equation will be, 14 + 8 – 5 = y
y = 17
So, There are 17 people on the bus.
Question 2.
Grandmother picked 4 times as many apples as pears. What is the difference in the number of apples and pears picked if she picked 8 pears?
Answer: the difference in the number of apples and pears is 24.
Explanation:
Given, Grandmother picked 4 times as many apples as pears.
the difference in the number of apples and pears picked if she picked 8 pears is
let the unknown be y ,
y = 4 × 8 = 32
Then she has 32 apples and 8 pears
That means 32 – 8 = 24
So, the difference in the number of apples and pears is 24.
Independent Practice
Algebra Write an equation with a letter for the unknown. Then solve. Check for reasonableness.
Question 3.
Whitney went to the hobby store. She bought 3 model airplanes for $4 each. She received $8 in change. How much money did she start with?
Answer: She has $20 from the start
Explanation:
Given, Whitney went to the hobby store.
She bought 3 model airplanes for $4 each.
let the unknown be y
3 × 4 = y
y = 12
She received $8 in change.
Then $20 – $12 = $8
She has $20 from the start
check $12 + $8 = $20 .
Question 4.
Mr. Robbins gave 9 students one pencil each. That afternoon, he gave 5 more students one pencil each. Now he has 15 pencils. How many pencils did he start with?
Answer: He started with 29 pencils
Explanations:
Given, Mr. Robbins gave 9 students one pencil each.
That afternoon, he gave 5 more students one pencil each. Now he has 15 pencils.
let the unknown be y ,
9 + 5 + 15 = y
y = 29
He started with 29 pencils
Check, 9 + 5 + 15 = 29.
Question 5.
Look at the table. How many more pens does Carmen have than Pamela and Cesar have together?
Answer: Carmen have 4 more pens than Pamela and Cesar have together
Explanation:
Given, Pamela has 7 pens.
Cesar has 9 pens,
Carmen has 20 pens
Pamela and Cesar together have 7 + 9 = 16
Carmen has 20 pens , then , 20 – 16 = 4
So, Carmen have 4 more pens than Pamela and Cesar have together.
Algebra Circle the correct equation. Then solve the problem.
Question 6.
Molly earns $10 each week for babysitting. She spends $3 of that each week and saves the rest. How much money does she save after 8 weeks?
($10 – $3) × 8 = m
$10 – $3 × 8 = m
Answer: Molly has $56 after 8 weeks.
Explanation:
Given, Molly earns $10 each week for babysitting.
She spends $3 of that each week and saves the rest.
The the equation will be , ($10 – $3) × 8 = m
Here, m is the unknown
The parentheses are to differentiate between the money spent on each week.
7 × 8 = m
m = 56.
So, Molly has $56 after 8 weeks.
Question 7.
The first 5 pages of Angel’s photo album are filled with 8 photos each. The next page has only 7 photos. How many photos are on the 6 pages?
5 × 8 + 7 = p
5 × 8 + p = 40
Answer: There are 47 photos on the 6 pages.
Explanation:
Given, The first 5 pages of Angel’s photo album are filled with 8 photos each.
The next page has only 7 photos.
The equation will be, 5 × 8 + 7 = p
40 + 7 = p
p = 47
So, There are 47 photos on the 6 pages.
Algebra Find each unknown.
Question 8.
k – 9 = 9
k = _____________
Answer: 18
Explanation:
Given, k – 9 = 9
k = 9 + 9 = 18
So, k = 18.
Question 9.
45 ÷ v = 5
v = ______________
Answer: 9
Explanation:
Given, 45 ÷ v = 5
v = 45 ÷ 5 = 9
So, v= 9
Question 10.
9 + 2 = 12 – q
q = _____________
Answer: 1
Explanation:
Given, 9 + 2 = 12 – q
q = 12 – 11 = 1
So, q = 1.
Problem Solving
Mathematical PRACTICE Check for Reasonableness Write an equation with a letter for the unknown. Then solve. Check for reasonableness.
Question 11.
It rained 6 inches each month for the last 6 months. How much will it need to rain this month for the total rainfall to be 43 inches?
Answer: The rainfall of this month should be 7 inches.
Explanation:
Given, It rained 6 inches each month for the last 6 months.
Then expression is 6 × 6 = 36
Let the unknown be y ,
( 6× 6 ) + y = 43
36 + y = 43
y = 43 – 36
y = 7
So, The rainfall of this month should be 7 inches.
check, replace y = 7
36 + y = 43
36 + 7 = 43
43 = 43.
So, the answer is reasonable.
Question 12.
There were 48 oranges in 6 equal layers in a box. Mother took some oranges from the top layer for snacks. How many oranges did mother take if there are 5 oranges left on the top layer?
Answer: the mother took 3 oranges.
Explanation:
Given, There were 48 oranges in 6 equal layers in a box.
Mother took some oranges from the top layer for snacks.
Then, each layer has 8 oranges,
if there are 5 oranges on the top layer then,
let the unknown be y ,
(48 ÷ 6) – y = 5
8 – y = 5
y = 3
So, the mother took 3 oranges.
check, y = 3
8 – y = 5
8 – 3 = 5
5 = 5
So, The answer is reasonable.
HOT Problems
Question 13.
Mathematical PRACTICE Make Sense of Problems Amelia made 10 fruit kabobs. She divided 20 cherries equally among half of the kabobs. How many cherries did each kabob get?
Answer: Each kabob gets 4 cherries.
Explanation:
Given, Amelia made 10 fruit kabobs.
She divided 20 cherries equally among half of the kabobs.
then, 20 ÷ ( 10 ÷ 2 ) = y
20 ÷ 5 = y
y = 4.
So, Each kabob gets 4 cherries.
Question 14.
Mathematical PRACTICE Find the Error Look back at Exercise 6. Explain why the other choice is incorrect.
Answer: Because There are no parentheses for $10 – $3 × 8 = m.
Explanation:
Given, Molly earns $10 each week for babysitting.
She spends $3 of that each week and saves the rest.
The the equation will be , ($10 – $3) × 8 = m
Here, m is the unknown
The parentheses are to differentiate between the money spent on each week.
7 × 8 = m
m = 56.
So, Molly has $56 after 8 weeks.
Question 15.
Building on the Essential Question Why is it important to perform the operations in an equation in a certain order?
Answer: Subtraction, multiplication, and division are all examples of operations.) The order of operations is important because it guarantees that people can all read and solve a problem in the same way.
Explanation:
for example,
(48 ÷ 6) – y = 5
8 – y = 5
y = 3
Here, the order is solve with in parentheses first. and then for the mathematical operations.
McGraw Hill My Math Grade 3 Chapter 9 Lesson 8 My Homework Answer Key
Practice
Algebra Find each unknown.
Question 1.
48 ÷ 6 + m = 11
m = ______________
Answer: m = 3.
Explanation:
Given, 48 ÷ 6 + m = 11
8 + m = 11
m = 11 – 8 = 3
So, m = 3.
Question 2.
37 – 9 = h × 4
h = ________________
Answer: h = 7
Explanation:
Given, 37 – 9 = h × 4
28 = h × 4
h = 28 ÷ 4 = 7
So, h = 7.
Question 3.
20 + 20 = 4 × w
w = _________________
Answer: w = 10
Explanation:
Given, 20 + 20 = 4 × w
40 = 4 × w
w = 40 ÷ 4 = 10
So, w = 10
Question 4.
(4 + 2) × r = 54
r = __________________
Answer: r = 9
Explanation:
Given, (4 + 2) × r = 54
6 × r = 54
r = 54 ÷ 6 = 9
So, r = 9
Problem Solving
Mathematical PRACTICE Check for Reasonableness Write an equation with a letter for the unknown. Then solve. Check for reasonableness.
Question 5.
The football team had its photo taken. There are 3 rows of 8 players each. The fourth row has 6 players. How many players are in the team photo?
Answer: There are 30 players in the team photo.
Explanation:
Given, The football team had its photo taken.
There are 3 rows of 8 players each. The fourth row has 6 players.
The equation will be ( 3 × 8 ) + 6 = y
Let the y be the unknown
24 + 6 = y
y = 30
So, There are 30 players in the team photo.
check, y= 30
( 3 × 8 ) + 6 = y
( 3 × 8 ) + 6 = 30
24 + 6 = 30
30 = 30
So, the answer is reasonable.
Question 6.
Mrs. Dove made 15 pancakes. She divided them evenly among Kurt, Joan, and David. Kurt and Joan ate all of their pancakes, but David did not eat some of his. There were 2 pancakes left on David’s plate. How many pancakes did he eat?
Answer: David ate 3 pancakes
Explanation:
Given, Mrs. Dove made 15 pancakes. She divided them evenly among Kurt, Joan, and David.
Kurt and Joan ate all of their pancakes,
There were 2 pancakes left on David’s plate.
Let the unknown be y
( 15 ÷ 3 ) – 2 = y
5 – 2 = y
y = 3
So, David ate 3 pancakes
Check, y = 3
5 – 2 = y
5 – 2 = 3
3 = 3
so, The answer is reasonable.
Question 7.
Keira has 83 spelling words to study in 8 weeks. She already knows 3 words. She will study the same number of words each week. How many spelling words will Keira study each week?
Answer: 10
Explanation:
Given, Keira has 83 spelling words to study in 8 weeks.
She already knows 3 words. She will study the same number of words each week.
Let the unknown be y
(83 – 3 ) ÷ 8 = y
y = 80 ÷ 8
y = 10
So, She has to read 10 spelling words each week.
check, y = 10
y = 80 ÷ 8
10 = 80 ÷ 8
10 = 10.
So, The answer is reasonable.
Question 8.
Grant bought 6 packs of stickers for $2 each. How much change will Grant receive if he pays with three $5 bills?
Answer: $3
Explanation:
Given, Grant bought 6 packs of stickers for $2 each.
6 × 2 = 12
if he pays with three $5 bills
3 × 5 = 15
He receives 15 – 12 = 3
So, Grant receives the change of $3.
Test Practice
Question 9.
Isaac has taken five quizzes. He scored 8 points on each of the first 4 quizzes. He scored y points on the fifth quiz. He has scored a total of 41 points. Which equation represents the situation?
(A) 41 ÷ 5 = y
(B) 8 × 4 ÷ 5 = y
(C) 4 × 8 + y = 41
(D) 41 ÷ 4 + y = 8
Answer: C
Explanation:
Given, Isaac has taken five quizzes. He scored 8 points on each of the first 4 quizzes.
He scored y points on the fifth quiz. He has scored a total of 41 points.
Let the unknown be y
4 × 8 + y = 41
32 + y = 41
y = 41 – 32
y = 9.
So, Option C is correct option.