Algebra story problems

Ages, consecutive numbers, coins and values, mixtures, systems and work rates — the stories that are only tractable once you name the unknown.

6 sheets · 30 questions · one answer key · 8 pages

Recommended for grades 7–8

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Age problems Sheet 1 of 6

Word problemsAge problems

Name: Date:

Read each problem. Write the answer.

1The pine tree is 15 years old today. In 7 years, the oak tree will be 3 times as old as the pine tree.How old is the oak tree today?

2The beech tree is 29 years old today. In 8 years, the elm tree will be 3 times as old as the beech tree.How old is the elm tree today?

3The elm tree has stood twice as long as the beech tree, and the two together are 78 years old.How old is the beech tree?

4The oak tree has stood 48 years longer than the pine tree, and is 5 times as old.How old is the pine tree?

5Elena is 6 years old today. In 5 years, Omar will be twice as old as Elena.How old is Omar today?

Word problemsConsecutive numbers

Name: Date:

Read each problem. Write the answer.

1The numbers on 3 consecutive pages of a book add up to 81.What is the middle page number?

2Adding 3 consecutive even numbers gives 126.What is the smallest number?

3The numbers on 3 consecutive houses on the odd side of a street add up to 135.What is the middle house number?

4Adding 3 consecutive even numbers gives 162.What is the middle number?

5The numbers on 3 consecutively numbered raffle tickets add up to 204.What is the middle ticket number?

Word problemsValue problems

Name: Date:

Read each problem. Write the answer.

1In a treasure hunt, a rare gem is worth 15 points and a common gem is worth 2 points. A player scored 174 points from 10 rare gems and some common gems.How many common gems did the player find?

2In a recycling contest, a glass bottle is worth 25 points and an aluminum can is worth 2 points. A player collected 12 glass bottles and 9 aluminum cans.How many points in total?

3In a treasure hunt, each rare gem is worth 25 points and each common gem is worth 3 points. Altogether, a player found 3 rare gems and 8 common gems.How many points is that in total?

4A gold coin in an arcade game scores 10 points, while a silver coin scores 2. A player scored 130 points in all, from 12 gold coins and some silver coins.How many silver coins did the player collect in total?

5A hard question in a quiz scores 25 points, while an easy question scores 3. One player answered 6 hard questions and 10 easy questions.How many points did the player score altogether?

Word problemsMixtures

Name: Date:

Read each problem. Write the answer.

1A stall pours 4 liters of 25% orange juice together with 5 liters of 52% orange juice.What is the concentration of the mixture?

2The blend uses 5 kg of milk chocolate at $53 a kg and 2 kg of dark chocolate at $60 a kg.What is the price per kg of the blend?

3A 9-liter dispenser is filled with 4 liters of 39% pineapple juice and 5 liters of 48% pineapple juice.What is the concentration of the mixture?

4The blend uses 6 kg of hazelnuts at $40 a kg and 3 kg of macadamias at $49 a kg.What is the price per kg of the blend?

5An 11-liter dispenser is filled with 5 liters of 30% cranberry juice and 6 liters of 63% cranberry juice.What is the concentration of the mixture?

Word problemsSystems of equations

Name: Date:

Read each problem. Write the answer.

1One shopper buys 4 notebooks and 4 muffins for $72. Another buys 3 notebooks and 4 muffins for $63.What is the price of one notebook and one muffin?One notebookOne muffin

2The red jar holds 7 more marbles than the blue jar, and the two together hold 27 marbles.How many marbles are in the red jar, and how many in the blue jar?The red jarThe blue jar

3The green box and the yellow box hold 24 blocks altogether, and the green box has 16 more than the yellow box.How many blocks are in each?The green boxThe yellow box

4Together, 5 sandwiches and 4 bagels cost $49. On a second visit, 2 sandwiches and 5 bagels together cost $40.Find the price of one sandwich and one bagel.One sandwichOne bagel

5The top shelf and the bottom shelf hold 61 books altogether, and the top shelf has 15 more than the bottom shelf.How many books are in each?The top shelfThe bottom shelf

Word problemsWork rate

Name: Date:

Read each problem. Write the answer.

1One pipe fills a tank in 8 hours. A second pipe fills the same tank in 11 hours.In one hour with both pipes open, what fraction of the tank is filled?

2A tank is filled by two hoses: alone, one takes 6 hours and the other 5 hours. Both hoses are turned on at the same time.How long will it take the two hoses to fill the tank?

3A tank has two faucets. One faucet alone fills it in 5 hours, and the other alone fills it in 12 hours.What fraction of the tank do both faucets fill in one hour?

4A tank has two pipes. One pipe alone fills it in 4 hours, and the other alone fills it in 3 hours.What fraction of the tank do both pipes fill in one hour?

5A tank is filled by two pumps: alone, one takes 3 hours and the other 11 hours. Both pumps are turned on at the same time.How long will it take the two pumps to fill the tank?

Power Pack · Algebra story problemsAnswer key

Age problems

1. 15 + 7 = 22, then 3 × 22 = 66, then 66 − 7 = 59 years2. 29 + 8 = 37, then 3 × 37 = 111, then 111 − 8 = 103 years3. 2 + 1 = 3, then 78 ÷ 3 = 26 years4. 5 − 1 = 4, then 48 ÷ 4 = 12 years5. 6 + 5 = 11, then 2 × 11 = 22, then 22 − 5 = 17 years

Consecutive numbers

1. 81 ÷ 3 = 272. 126 ÷ 3 = 42, then 42 − 2 = 403. 135 ÷ 3 = 454. 162 ÷ 3 = 545. 204 ÷ 3 = 68

Coin and value problems

1. 174 − 10 × 15 = 24, then 24 ÷ 2 = 12 common gems2. 12 × 25 + 9 × 2 = 318 points3. 3 × 25 + 8 × 3 = 99 points4. 130 − 12 × 10 = 10, then 10 ÷ 2 = 5 silver coins5. 6 × 25 + 10 × 3 = 180 points

Mixtures

1. 4 × 25 + 5 × 52 = 360, then 360 ÷ 9 = 40%2. 5 × 53 + 2 × 60 = 385, then 385 ÷ 7 = $553. 4 × 39 + 5 × 48 = 396, then 396 ÷ 9 = 44%4. 6 × 40 + 3 × 49 = 387, then 387 ÷ 9 = $435. 5 × 30 + 6 × 63 = 528, then 528 ÷ 11 = 48%

Power Pack · Algebra story problemsAnswer key

Systems of equations

1. a = notebook, b = muffin: 4 × (3a + 4b = 63) → 12a + 16b = 252, 3 × (4a + 4b = 72) → 12a + 12b = 216; subtract to remove a → 4b = 36, so b = 9; then 4a + 4 × 9 = 72, so a = 9 — a notebook costs $9 and a muffin costs $92. (27 + 7) ÷ 2 = 17, then 27 − 17 = 10, so 17 and 10 marbles3. (24 + 16) ÷ 2 = 20, then 24 − 20 = 4, so 20 and 4 blocks4. a = sandwich, b = bagel: 5 × (2a + 5b = 40) → 10a + 25b = 200, 2 × (5a + 4b = 49) → 10a + 8b = 98; subtract to remove a → 17b = 102, so b = 6; then 5a + 4 × 6 = 49, so a = 5 — a sandwich costs $5 and a bagel costs $65. (61 + 15) ÷ 2 = 38, then 61 − 38 = 23, so 38 and 23 books

Work problems

1. + = 2. + = , so 1 ÷ = 2 hours3. + = 4. + = 5. + = , so 1 ÷ = 2 hours

Algebra story problems

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