Algebra Word Problems - Page 6

Algebra Word Problems
• Page 6
51.
Bill gave $\frac{1}{10}$ th of his salary to the poor people. What is he left with?
 a. $$\frac{9x}{10}$ b.$10$x$ c. $$\frac{x}{10}$ d.$$\frac{x}{2}$

Let $x be the salary of Bill. The amount he gave to the poor = 1 / 10 × x = x / 10. [Multiply x with 1 / 10.] The amount left with Bill = Salary Bill got - The amount he gave to the poor = x - x / 10 [Substitute the values.] = 10x / 10 - x / 10 [Multiply and divide the numerator and denominator of the first fraction by 10.] = 9x / 10 [Subtract the numerators.] Correct answer : (1) 52. Find Nancy's age, if she was 17, 17 years ago .  a. 34 b. 39 c. 24 d. 44 Solution: Let x be the present age of Nancy. The present age of Nancy = Nancy's age 17 years ago + 17 [Write the algebraic expression.] x = 17 + 17 [Substitute.] x = 34 [Add.] So, Nancy is 34 years old. Correct answer : (1) 53. Paul bought 5 pencils. Find the cost of one pencil, if the cost of ten pencils was$10.
 a. $3 b.$1 c. $4 d.$2

Solution:

Let a be the cost of one pencil.

The cost of one pencil = Cost of ten pencils ÷ number of pencils
[Write an algebraic expression.]

a = 10 ÷ 5
[Substitute.]

a = 2
[Divide 10 with 5.]

So, the cost of one pencil is $2. Correct answer : (4) 54. Ethan, Sam, Josh, and George went to a movie. Find the cost of one ticket, if they paid$48 for four tickets.
 a. $17 b.$12 c. $15 d.$14

Solution:

Let y be the cost of one ticket.

The cost of one ticket = cost of all the tickets ÷ number of tickets
[Write an Algebraic expression.]

y = 48 ÷ 4
[Substitute.]

y = 12
[Divide 48 with 4.]

So, the cost of one ticket is $12. Correct answer : (2) 55. Christina visits a food store. She wants to buy 14 burgers. Find the cost of 14 burgers if the cost of one burger is$4.
 a. $56 b.$61 c. $51 d.$66

Solution:

Let b be the cost of 14 burgers.

Cost of 14 burgers = cost of one burger x 14
[Write an algebraic expression.]

b = 4 x 14
[Substitute.]

b = 56
[Multiply.]

So, the cost of 14 burgers is $56. Correct answer : (1) 56. Edward spends $\frac{4}{9}$ of his salary on luxuries. How much is left with him?  a. $\frac{4}{5}$ of his salary b. $\frac{5}{9}$ of his salary c. $\frac{1}{9}$ of his salary d. $\frac{4}{9}$ of his salary Solution: Let '$p' be the salary of Edward.

The amount he spends on luxuries = 4 / 9 x p = 4p / 9 .
[Multiply p with 4 / 9 .]

The amount left with Edward = Salary Edward gets - the amount he spends on luxuries.

= p - 4p9
[Substitute the values.]

=9p9- 4p9
[Multiply and divide the numerator and denominator of the first fraction by 9.]

= 5p9
[Subtract the numerators.]

57.
Lydia has $68. He buys 2 shirts that cost$13 each. How much is she left with after buying the shirts?
 a. $42 b.$66 c. $72 d.$70

Solution:

Let x be the money she is left with.

Money left = money Lydia has - (cost of one shirt × number of shirts)
[Write an algebraic expression.]

x = $68 - (13 × 2) [Substitute.] x = 68 - 26 [Multiply.] x = 42 [Subtract 26 from 68.] So, Lydia is left with$42.

58.
William and Tim ran a fundraising campaign. William collected $6 more than Tim. How much did William collect, if Tim collected$12?
 a. $19 b.$21 c. $23 d.$18

Solution:

Let y be the money William collected.

Money collected by William = money collected by Tim + extra dollars collected by William
[Write an Algebraic expression.]

y = 12 + 6
[Substitute.]

y = 18

So, William collected \$18.

59.
Jessica buys a box of marbles. The box has 5 dozen marbles. Find the number of marbles in the bag.
 a. 48 b. 72 c. 60 d. 66

Solution:

Let x be the number of marbles.

Number of marbles in the bag = number of dozens x 12
[Write an algebraic expression.]

x = 5 x 12
[Convert dozens to number as 1 dozen = 12.]

x = 60
[Multiply.]

Number of marbles in the bag = 60.

60.
How many students are there in Mrs. Zelma's class, if there are 24 boys and 26 girls in the class?
 a. 54 b. 48 c. 50 d. 56

Solution:

Let b be the number of students in Mrs. Zelma's class.

Number of students in Mrs. Zelma's class = number of boys + number of girls
[Write an algebraic equation.]

b = 24 + 26
[Substitute.]

b = 50