MULTI STEP ALGEBRA WORD PROBLEMS

Problem 1 :

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?

Solution :

Let x be the number of students in each bus.

From the given information, we have

6x + 7 = 331

Subtract 7 from both sides.

6x = 324

Divide both sides by 6.

x = 54

There were 54 students in each bus.

Problem 2 :

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?

Solution :

Let x be the cost of each pencil.

From the given information, we have

7x + 10 = 24

Subtract 10 from both sides.

7x = 14

Divide both sides by 7.

x = 2

Each pencil costed $2.

Problem 3 :

The sum of three consecutive numbers is 72. What is the smallest of these numbers?

Solution :

The three consecutive numbers can be assumed as

x, (x + 1), (x + 2)

Given : The sum of three consecutive numbers is 72.

x + (x + 1) + (x + 2) = 72

x + x + 1 + x + 2 = 72

3x + 3 = 72

Subtract 3 from both sides.

3x = 69

Divide both sides by 3.

x = 23

The smallest of of the three consecutive numbers is 23.

Problem 4 :

The sum of three consecutive even numbers is 48. What is the smallest of these numbers?

Solution :

The three consecutive even numbers can be assumed as

x, (x + 2), (x + 4)

Given : The sum of three consecutive even numbers is 48.

x + (x + 2) + (x + 4) = 48

x + x + 2 + x + 4 = 48

3x + 6 = 48

Subtract 6 from both sides.

3x = 42

Divide both sides by 3.

x = 14

The smallest of of the three consecutive even numbers is 14.

Problem 5 :

You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost?

Solution :

Let x be the cost of each eraser.

From the given information, we have

5 + 4x = 25

Subtract 5 from both sides.

4x = 20

Divide both sides by 4.

x = 5

Each eraser costed $5.

Problem 6 :

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start?

Solution :

Let x be the number of boxes Maria started with.

From the given information, we have

Multiply both sids by 2.

x + 7 = 44

Subtract 7 from both sides.

x = 37

Maria started with 37 boxes.

Problem 7 :

Sumalee won 40 super bouncy balls playing horseshoes at her school's game night. Later, she gave two to each of her friends. She only has 8 remaining. How many friends does she have?

Solution :

Let x be the number of friends Sumalee has.

From the given information, we have

2x + 8 = 40

Subtract 8 from both sides.

2x = 32

Divide both sides by 2.

x = 16

Sumalee has 16 friends.

Problem 8 :

Imani spent half of her weekly allowance playing mini-golf. To earn more money her parents let her wash the car for $4. What is her weekly allowance if she ended with $12?

Solution :

Let x be Imani's weekly allowance.

From the given information, we have

Subtract 4 from both sides.

Multiply both sides by 2.

x = 16

Imani's weekly allowance is $16.

Problem 9 :

Aliyah had some candy to give to her four children. She first took ten pieces for herself and then evenly divided the rest among her children. Each child received two pieces. With how many pieces did she start?

Solution :

From the given information, number of pieces Aliyah started with :

= 10 + 4(2)

= 10 + 8

= 18

Problem 10 :

How old am I if 400 reduced by 2 times my age is 244?

Solution :

Let me be x years old.

From the given information, we have

400 - 2x = 244

Subtract 400 from both sides.

-2x = -156

Divide both sides by -2.

x = 78

I am 78 years old.

Problem 11 :

Jill sold half of her comic books and then bought sixteen more. She now has 36. With how many did she begin?

Solution :

Let x be the number of books Jill started with.

From the given information, we have

Subtract 16 from both sides.

Multiply both sides by 2.

x = 40

Jill began with 40 books.

Problem 12 :

For a field trip 4 students rode in cars and the rest filled nine buses. How many students were in each bus if 472 students were on the trip?

Solution :

Let x be the number of students in each bus.

From the given information, we have

4 + 9x = 472

Subtract 4 from both sides.

9x = 468

Divide both sides by 9.

x = 52

There were 52 students in each bus.

Problem 13 :

On Tuesday Shanice bought five hats. On Wednesday half of all the hats that she had were destroyed. On Thursday there were only 17 left. How many did she have on Monday?

Solution :

Let x be the number of hats Shanice had on monday.

From the given information, we have

Multiply both sides by 2.

x + 5 = 34

Subtract 5 from both sides.

x = 29

Problem 14 :

The cooking club made some pies to sell at a basketball game to raise money for the new math books. The cafeteria contributed four pies to the sale. Each pie was then cut into five pieces and sold. There were a total of 60 pieces to sell. How many pies did the club make?

Solution :

Let x be the number of pies the cooking club made.

From the given information, we have

5x + 4(5) = 60

5x + 20 = 60

Subtract 20 from both sides.

5x = 40

Divide both sides by 5.

x = 8

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