All the solutions provided in **McGraw Hill Math Grade 4 Answer Key PDF Chapter 2 Lesson 9 Solve Multi-Step Word Problems** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 2 Lesson 9 Solve Multi-Step Word Problems

**Math in My World**

Example 1

The music club had $390 in their account. At the concert, they earned $472. Afterwards, they had to pay $75 to rent the stage and $102 for the rental equipment. How much is in their account now?

Write an equation.

When more than one step is involved, add and subtract in order from left to right.

So, the account now has $685

Answer: An estimate is $400 + $500 – $100 – $100 = $700

This is close to the actual amount, which is $685.

Explanation:

Given, The music club had $390 in their account. At the concert, they earned $472.

Afterwards, they had to pay $75 to rent the stage and $102 for the rental equipment.

The ones they are earning are the add ups and the ones they are spending are to be subtracted

Let the variable be y , which we have to find out,

So, We can write the equation as 390 + 472 – 75 – 102 = y .

y = 862 -75 – 102

y = 787 – 102

y = 685,

Thus, The amount left with them is $685

To check for an estimate, round the numbers to the nearest hundreds we get,

$400 + $500 – $100 – $100 = $700

This is close to the actual amount, which is $685. So, the answer is reasonable.

Example 2

Twenty people got on the bus at the first stop. At the second stop, 14 people got off the bus, and 5 people got on the bus. At the third stop, 2 people got off the bus, and some people got on the bus. Then there were 24 people on the bus. How many people got on the bus at the third stop?

Write an equation.

The letter b can be used as a variable to represent the unknown.

**Find the unknown.**

So, 15 people got on the bus at the third stop.

Answer: Totally, 15 people got on the bus at the third stop.

Explanation:

Given, Twenty people got on the bus at the first stop.

At the second stop, 14 people got off the bus, and 5 people got on the bus.

At the third stop, 2 people got off the bus, and some people got on the bus.

Then there were 24 people on the bus

Here the people who are on the bus are the add ups and the ones who got off are to be subtracted

Let the variable be b.

The equation will be 20 – 14 + 5 – 2 + b = 24

6 + 5 – 2 + b = 24

11 – 2 + b = 24

9 + b = 24

b = 24 – 9

b = 15

So, 15 people got on the bus at the third stop.

**Talk Math**

Can you use any letter of the alphabet for a variable? Explain

Answer: Yes, Any letter or symbol can represent a variable, or unknown, as they’re sometimes called; it makes no difference whether you use a, k or x.

A variable is a symbol, often a letter, that is used to represent an unknown, or a number that is not known.

**Guided Practice**

Question 1.

**Algebra** Savannah had $15. She earned $20. Then, she bought a gift for 8. How much money does she have left? Write an equation to solve the problem. Use a variable for the unknown.

Answer: he have left with $27.

Explanation:

Given, Savannah had $15. She earned $20. Then, she bought a gift for 8.

Now, write up an equation for the money she has and earned as add ups , And her expenses as subtracts

We have to find how much money she left which will be the unknown variable Let the unknown variable be y,

Then, $15 + $20 – $8 = y

y = $35 – $8

y = $27

So, She have left with $27.

**Independent Practice**

**Algebra Write an equation to solve each problem. Use a variable for the unknown.**

Question 2.

Bailey had 75 beads. She used 20 of them on a necklace and 12 of them on a bracelet. Then she bought 25 more beads. How many beads does Bailey have now?

Answer: Bailey has 68 beads.

Explanation:

Given, Bailey had 75 beads. She used 20 of them on a necklace and 12 of them on a bracelet.

Then she bought 25 more beads.

The ones she had will be add ups and she used will be subtracts

To know , How many beads does Bailey have now , Let the Unknown variable be y

The equation will be, 75 – 20 – 12 + 25 = y

y = 55 – 12 + 25

y = 43 + 25

y = 68

So, Bailey has 68 beads.

Question 3.

Alex had $30. He spent $13 on a game and $5 on a poster. Then, he earned $8 doing chores for a week. How much money does Alex have now?

Answer: Alex has $20

Explanation:

Given, Alex had $30. He spent $13 on a game and $5 on a poster.

Then, he earned $8 doing chores for a week.

The money he had and earned will be the add ups and the money he spent will be the subtract,

To know ,How much money does Alex have now? Let the Unknown variable be y

Then, y = $30 – $13 – $5 + $8

y = $17 – $5 + $8

y = $12 + $ 8

y = $20

So, Alex has $20.

Question 4.

Hunter had 16 jars of paint. He used 2 of them on a painting. He bought 8 more jars. Then, he used some of the jars to make another painting. Now, Hunter has 15 jars of paint. How many jars did he use for the second painting?

Answer: He used 7 jars of paint for the second painting.

Explanation:

Given, Hunter had 16 jars of paint. He used 2 of them on a painting.

He bought 8 more jars. Then, he used some of the jars to make another painting.

Now, Hunter has 15 jars of paint.

To know, How many jars did he use for the second painting? Let the Unknown variable be y

Then, 16 – 2 + 8 – y = 15

We can write it as , y = 16 – 2 + 8 – 15

y = 14 + 8 – 15

y = 22 – 15

y = 7

So, He used 7 jars of paint for the second painting.

Question 5.

A restaurant served food to a large party. The manager is listing the total costs, shown below.

The total cost is $1,317. How much did the side dishes cost?

Answer: The cost of the side dishes are $327

Explanation:

Given, The total cost is $1,317

To know, How much did the side dishes cost? Let the Unknown variable be y

The prices of the items are the add ups and the total cost will be the subtract

Then, 452 + 388 + 150 – y = 1,317

We can write it as , y = 452 + 388 + 150 – 1,317

y = 1,317 – 990

y = 327

So, The cost of the side dishes are $327

**Problem Solving**

**Use a number cube to complete each number puzzle.**

Question 6.

Roll a number cube 4 times. Write one number in each box. Find the greatest value of the variable.

+ – + = b

b = ____

Answer: b = 9

Explanation:

Given, Roll a number cube 4 times

6 + 2 – 4 + 5 = b

b = 8 – 4 + 5

b = 4 + 5

b = 9.

Question 7.

Roll a number cube 6 times. Write one number in each box. Find the greatest value of the variable.

+ – + + – = y

y = ____

Answer: y = 9

Explanation:

Given, Roll a number cube 6 times.

5 + 3 – 2 + 6 + 1 – 4 = y

y = 8 – 2 + 6 + 1 – 4

y = 6 + 6 + 1 – 4

y= 13 – 4

y = 9.

**HOT problems**

Question 8.

**Mathematical PRACTICE 1 Make Sense of Problems** Victoria had some money in her wallet. She went to the mall and spent $8 on a stuffed animal, $7 on lunch, and $13 on a gift for her mom. Then her brother gave her $10. She bought a book for $15. Now she has $12. How much money did Victoria originally have in her wallet?

Answer: Victoria originally have $45 in her wallet.

Explanation:

She went to the mall and spent $8 on a stuffed animal, $7 on lunch, and $13 on a gift for her mom.

Then her brother gave her $10.

She bought a book for $15. Now she has $12.

To know, How much money did Victoria originally have in her wallet? Let the Unknown variable be y

Then, y – 8 – 7 – 13 +10 – 15 = 12

we can write it as y = 8 + 7 + 13 – 10 + 15 + 12

y = 28 – 10 + 15 + 12

y = 18 + 15 + 12

y = 45

So, Victoria originally have $45 in her wallet.

Question 9.

**? Building on the Essential Question** How can I use variables to describe real-world problems? Explain.

Answer: You can use a variable expression to describe a real world situation where one or more quantities have an unknown value or can change in value. To write a variable expression for a real world situation: Figure out which quantity in the situation is unknown and define a variable to represent the unknown quantity.

**Fluency Practice**

**Add.**

Question 1.

Answer: 92,987

Explanation:

To estimate

Given, 53,035 + 39,952

round to the nearest hundred we get

53,000 + 40,000 = 93,000

So, 93,000 is nearest to 92,987

Question 2.

Answer: 1,57,461

Explanation:

To estimate

Given, 94,225 + 63,236

round to the nearest hundred we get

94,000 + 63,000 = 157,000

So, 157,000 is nearest to 1,57,461

Question 3.

Answer: 1,19,601

Explanation:

To estimate

Given, 82,427 + 37,174

round to the nearest hundred we get

82,000 + 37,000 = 119,000

So, 119,000 is nearest to 1,19,601

Question 4.

Answer: 50,481

Explanation:

To estimate

Given, 32,472 + 18,009

round to the nearest hundred we get

32,000 + 18,000 = 50,000

So, 50,000 is nearest to 50,481

Question 5.

Answer: 1,35,164

Explanation:

To estimate

Given, 72,259 + 62,905

round to the nearest hundred we get

72,000 + 63,000 = 1,35,000

So, 1,35,000 is nearest to 1,35,164

Question 6.

Answer: 69,801

Explanation:

To estimate

Given, 52,372 + 17,429

round to the nearest hundred we get

52,000 + 17,000 = 69,000

So, 69,000 is nearest to 69,801

Question 7.

Answer: 77,744

Explanation:

To estimate

Given, 63,141 + 14,603

round to the nearest hundred we get

63,100 + 14,600= 77,700

So, 77,700 is nearest to 77,744

Question 8.

Answer: 59,099

Explanation:

To estimate

Given, 20,407 + 38,692

round to the nearest hundred we get

20,400 + 38,700 = 59,100

So, 59,100 is nearest to 59,099

Question 9.

Answer: 4,19,870

Explanation:

To estimate

Given, 367,028 + 52,842

round to the nearest hundred we get

367,000 + 52,900 = 4,19,900

So, 4,19,900 is nearest to 4,19,870

Question 10.

Answer: 5,03,437

Explanation:

To estimate

Given, 482,952 + 20,485

round to the nearest hundred we get

483,000 + 20,500 = 5,03,500

So, 5,03,500 is nearest to 5,03,437

Question 11.

Answer: 2,21,990

Explanation:

To estimate

Given, 137,953 + 84,037

round to the nearest hundred we get

138,000 + 84,000 = 2,22,000

So, 2,22,000 is nearest to 2,21,990

Question 12.

Answer: 9,06,182

Explanation:

To estimate

Given, 813,448 + 92,734

round to the nearest hundred we get

813,400 + 92,700 = 9,06,100

So, 9,06,100 is nearest to 9,06,182

Question 13.

Answer: 9,34,223

Explanation:

To estimate

Given, 103,374 + 824,849

round to the nearest hundred we get

103,300 + 824,800 = 9,28,100

So, 9,28,100 is nearest to 9,34,223

Question 14.

Answer: 7,45,110

Explanation:

To estimate

Given, 372,555 + 372,555

round to the nearest hundred we get

372,500 + 372,500 = 7,45,000

So, 7,45,000 is nearest to 7,45,110

Question 15.

Answer: 9,60,514

Explanation:

To estimate

Given, 218,662 + 741,852

round to the nearest hundred we get

218,600 + 741,900 = 9,60,500

So, 9,60,500 is nearest to 9,60,514

Question 16.

Answer: 8,46,009

Explanation:

To estimate

Given, 359,751 + 486,258

round to the nearest hundred we get

359,700 + 486,300 = 8,46,000

So, 8,46,000 is nearest to 8,46,009

Question 17.

Answer: 3,72,586

Explanation:

To estimate

Given, 118,577 + 254,009

round to the nearest hundred we get

118,500 + 254,000 = 3,72,500

So, 3,72,500 is nearest to 3,72,586

Question 18.

Answer: 9,91,110

Explanation:

To estimate

Given, 888,888 + 102,222

round to the nearest hundred we get

888,900 + 102,200 = 9,91,100

So, 9,91,100 is nearest to 9,91,110

Question 19.

Answer: 9,75,269

Explanation:

To estimate

Given, 328,805 + 646,464

round to the nearest hundred we get

328,800 + 646,400 = 9,75,264

So, 9,75,264 is nearest to 9,75,269

Question 20.

Answer: 5,89,542

Explanation:

To estimate

Given, 335,533 + 254,009

round to the nearest hundred we get

335,500 + 254,000 = 5,87,500

So, 5,87,500 is nearest to 5,89,542

**Fluency Practice**

**Subtract.**

Question 1.

Answer: 26,071

Explanation:

Given, 63,581 – 37,510 = 26,071

To check , we can add the subtrahend to the result

That is 26,071 + 37,510 = 63,581

Question 2.

Answer: 10,003

Explanation:

Given, 72,510 – 62,507 = 10,003

To check , we can add the subtrahend to the result

That is 10,003 + 62,507 =72,510

Question 3.

Answer: 66,564

Explanation:

Given, 82,404 – 15,840 = 66,564

To check , we can add the subtrahend to the result

That is 66,564 + 15,840 =82,404

Question 4.

Answer: 15

Explanation:

Given, 43,524 – 43,509 = 15

To check , we can add the subtrahend to the result

That is 15 + 43,509 =43,524

Question 5.

Answer: 13,693

Explanation:

Given, 42,824 – 29,131 = 13,693

To check , we can add the subtrahend to the result

That is 13,693 + 29,131 = 42,824

Question 6.

Answer: 14,220

Explanation:

Given, 34,108 – 19,888 = 14,220

To check , we can add the subtrahend to the result

That is 14,220 + 19,888 = 34,108

Question 7.

Answer: 730

Explanation:

Given, 13,546 – 12,816 = 730

To check , we can add the subtrahend to the result

That is 730 + 12,816 = 13,546

Question 8.

Answer: 16,306

Explanation:

Given, 45,850 – 29,544 = 16,306

To check , we can add the subtrahend to the result

That is 16,306 + 29,544 = 45,850

Question 9.

Answer: 2,90,333

Explanation:

Given, 237,482 – 52,851 = 2,90,333

To check , we can add the subtrahend to the result

That is 2,90,333 + 52,851 = 237,482

Question 10.

Answer: 2,89,000

Explanation:

Given, 321,123 – 32,123 = 2,89,000

To check , we can add the subtrahend to the result

That is 2,89,000 + 32,123 = 321,123

Question 11.

Answer: 53,916

Explanation:

Given, 137,953 – 84,037 = 53,916

To check , we can add the subtrahend to the result

That is 53,916 + 84,037 = 137,953

Question 12.

Answer: 3,25,542

Explanation:

Given, 338,200 – 12,658 = 3,25,542

To check , we can add the subtrahend to the result

That is 3,25,542 + 12,658 = 338,200

Question 13.

Answer: 1,22,124

Explanation:

Given, 825,385 – 703,261 = 1,22,124

To check , we can add the subtrahend to the result

That is 1,22,124 + 703,261 = 825,385

Question 14.

Answer: 4,35,859

Explanation:

Given, 651,851 – 215,992 = 4,35,859

To check , we can add the subtrahend to the result

That is 4,35,859 + 215,992 = 651,851

Question 15.

Answer: 47,610

Explanation:

Given, 453,166 – 405,556 = 47,610

To check , we can add the subtrahend to the result

That is 47,610 + 405,556 = 453,166

Question 16.

Answer: 14,610

Explanation:

Given, 212,894 – 198,284 = 14,610

To check , we can add the subtrahend to the result

That is 14,610 + 198,284 = 212,894

Question 17.

Answer: 2,07,439

Explanation:

Given, 489,255 – 281,816 = 2,07,439

To check , we can add the subtrahend to the result

That is 2,07,439 + 281,816 = 489,255

Question 18.

Answer: 90,038

Explanation:

Given, 258,914 – 168,876 = 90,038

To check , we can add the subtrahend to the result

That is 90,038 + 168,876 = 258,914

Question 19.

Answer: 1,85,999

Explanation:

Given, 545,248 – 359,249 = 1,85,999

To check , we can add the subtrahend to the result

That is 1,85,999 + 359,249 = 545,248

Question 20.

Answer: 1,16,283

Explanation:

Given, 605,060 – 488,777 = 1,16,283

To check , we can add the subtrahend to the result

That is 1,16,283 + 488,777 = 605,060.