Solving Linear Equations - Word Problems-Algebra1-Solved Examples

Solved Examples and Worksheet for Solving Linear Equations - Word Problems

Q1Arthur breaks a stick that is 50 cm into two pieces. Find the length of one piece if the length of other piece is 28 cm.

A. 22 cm
B. 27 cm
C. 32 cm
D. 17 cm

Solutions

Step: 1

Let l be the length of the piece.

Step: 2

28 + l = 50

[Original equation.]

Step: 3

28 + l - 28 = 50 - 28

[Subtract 28 from each side.]

Step: 4

l = 22

[Simplify.]

Step: 5

So, the length of the other piece is 22 cm.

Correct Answer is : 22 cm

Q2Two boxes of pineapples together weigh 666 lb. If one of them weighs 285 lb, then find the weight of the second box.

A. 381 lb
B. 388 lb
C. 371 lb
D. 384 lb

Solutions

Step: 1

Let w be the weight of the second box.

Step: 2

285 + w = 666

[Write a linear equation for the total weight of the two boxes.]

Step: 3

285 + w - 285 = 666 - 285

[Subtract 285 from each side.]

Step: 4

w = 381

[Simplify.]

Step: 5

So, the weight of the second box, w is 381 lb.

Correct Answer is : 381 lb

Q3Andrew bought a shirt at a price of $3 less than that mentioned on the tag. If he spent $39 for the shirt, then what was the price on the tag?

A. $42
B. $39
C. $36
D. None of the above

Solutions

Step: 1

Let x be the price on the tag.

Step: 2

The price Andrew paid for the shirt = $(x - 3)

Step: 3

x - 3 = 39

[Write an equation.]

Step: 4

x - 3 + 3 = 39 + 3

[Add 3 on each side.]

Step: 5

x = 42

[Simplify.]

Step: 6

The price on the tag is $42.

Correct Answer is : $42

Q4Tim went on a trip in his car. Gasoline costs $2 per gallon. For his trip, Tim spent $34 on gasoline. How many gallons of gasoline did he use?

A. 15
B. 17
C. 19
D. 13

Solutions

Step: 1

Let p be the gallons of gasoline consumed for Tim's trip

Step: 2

34 = 2 × p

[Write an equation.]

Step: 3

342 = (2 × p)2

[Divide each side by 2.]

Step: 4

17 = p

[Simplify.]

Step: 5

So, 17 gallons of gasoline was consumed on Tim's trip

Correct Answer is : 17

Q5Ethan is 7 years younger than George. What is George's age if Ethan is 50 years old?

A. 58
B. 57
C. 43
D. 44

Solutions

Step: 1

Let x be the age of George, then the age of Ethan is x - 7.

Step: 2

x - 7 = 50

[Write an equation.]

Step: 3

x - 7 + 7 = 50 + 7

[Add 7 to each side.]

Step: 4

x = 57

[Simplify.]

Step: 5

The age of George is 57 years.

Correct Answer is : 57

Q6Rachel's income is $5400. If her expenditure is $210, then find her savings.

A. $5175
B. $5190
C. $5210
D. $5205

Solutions

Step: 1

Let 's' be the savings of Rachel.

Step: 2

Savings + Expenditure = Total income.

Step: 3

s + 210 = 5400

[Substitute the values.]

Step: 4

s + 210 - 210 = 5400 - 210

[Subtract 210 from each side to isolate s.]

Step: 5

s = 5190

[Simplify.]

Step: 6

So, the savings of Rachel is $5190.

Correct Answer is : $5190

Q7A man sold an article for a loss of 15 of the cost. What was the cost of the article, if the loss occurred was $187?

A. $945
B. $940
C. $202
D. $ 935

Solutions

Step: 1

Let p be the cost of the article.

Step: 2

15 x p = 187

[Original Equation.]

Step: 3

p5 x 5 = 187 x 5

[Multiply each side by 5.]

Step: 4

p = 935

[Simplify.]

Step: 5

The cost of the article is $935.

Correct Answer is : $ 935

Q8How many bottles, each holding 4 fluid ounces, are needed to hold 2 quarts of cider?(1 Quart = 32 fluid ounces)
A. 16
B. 17
C. 18
D. 15

Solutions

Step: 1

Quantity of cider in each bottle x No. of bottles = Total Quantity of cider in all bottles.

Step: 2

Let n be the number of bottles.

Step: 3

4 x n = 2 x 32

[Original Equation, since 1 Quart = 32 fluid ounces.]

Step: 4

4n = 64

Step: 5

4n4 = 644

[Divide each side by 4.]

Step: 6

n = 16

[Simplify.]

Step: 7

The number of bottles needed to hold 2 quarts of cider is 16.

Correct Answer is : 16

Q9How much does a full-carton of biscuits cost, if one half of a carton of biscuits costs $130?

A. $270
B. $280
C. $290
D. $260

Solutions

Step: 1

Let b be the cost of a full-carton of biscuits.

Step: 2

b2 = 130

[Write an equation.]

Step: 3

b2 × 2 = 130 × 2

[Multiply each side by 2.]

Step: 4

b = 260

[Simplify.]

Step: 5

The cost of a full-carton of biscuits is $260.

Correct Answer is : $260

Q10Rachel bought take-out sandwiches for lunch at $20. She also paid some money for tax and tip. The total bill came up to $24. How much did she pay for tax and tip?

A. $4
B. $5
C. $3
D. $2

Solutions

Step: 1

Let, t be the money Rachel paid for tax and tip.

Step: 2

20 + t = 24

[Original equation.]

Step: 3

20 + t - 20 = 24 - 20

[Subtract 20 from each side.]

Step: 4

t = 4

[Simplify.]

Step: 5

Rachel paid $4 for tax and tip.

Correct Answer is : $4

Q11Sunny had $9656 in his bank account. He deposited some money and the new balance was $18785. How much did Sunny deposit in his account?

A. $9129
B. $8979
C. $9329
D. $9229

Solutions

Step: 1

New balance = previous balance + deposited amount

Step: 2

Let d be the amount deposited in the bank.

Step: 3

9656 + d = 18785

[Equation.]

Step: 4

9656 + d - 9656 = 18785 - 9656

[Subtract 9656 from each Side.]

Step: 5

d = 9129

[Simplify.]

Step: 6

Sunny deposited $9129 in his account.

Correct Answer is : $9129

Q12Team-A won 6 games more than Team-B in a games competition held by the school management. How many games had Team-B won, if Team-A won 8 games?
A. 4
B. 3
C. 2
D. 1

Solutions

Step: 1

Number of games won by Team-A = Number of games won by Team-B + 6

Step: 2

Let x be the Number of games won by Team-B.

Step: 3

x + 6 = 8

[Equation.]

Step: 4

x + 6 - 6 = 8 - 6

[Subtract 6 from each side.]

Step: 5

x = 2

[Simplify.]

Step: 6

Team-B won 2 games.

Correct Answer is : 2

Q13The average age of 13 boys is 4 years. What is the sum of their ages?
A. 62 years
B. 52 years
C. 42 years
D. 72 years

Solutions

Step: 1

Average age = Sum of their ages Number of boys

[In words.]

Step: 2

Let s be the sum of their ages.

Step: 3

4 = s13

[Equation.]

Step: 4

4 x 13 = ( s13) x 13

[Multiply each side by 13 to isolate x.]

Step: 5

52 = s

[Simplify.]

Step: 6

So, sum of the ages of 13 boys is 52 years.

Correct Answer is : 52 years

Q14Josh can complete a job in 45 days. In how many days Andrew can complete the same job, if he takes 14 days more than Josh does?

A. 77 days
B. 59 days
C. 71 days
D. 53 days

Solutions

Step: 1

Number of days taken by Andrew = Number of days taken by Josh + 14

Step: 2

Let d = the number of days taken by Andrew

Step: 3

d = 14 + 45

[Equation.]

Step: 4

d = 59

[Simplify.]

Step: 5

Andrew can complete the same work in 59 days.

Correct Answer is : 59 days

Solved Examples and Worksheet for Solving Linear Equations - Word Problems

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