# Algebraic Expressions Worksheets - Page 2

Algebraic Expressions Worksheets
• Page 2
11.
Smith earns $1,275 per month plus an 8% commission on his sales. He sold $x$ dollars of merchandise last month. Which equation can be used to find his total earnings of last month ($y$)?  a. $y$ = (1,275 + 0.08)$x$ b. $y$ = $x$ + 0.08$x$ c. $y$ = 1,275 + 0.08$x$ d. $y$ = 0.08(1,275) + $x$ #### Answer: (c) Correct answer : (3) 12. A waiter earned$64 for 8 hours of work, including $28 in tips. Which equation helps you to find his hourly wage?  a. $w$ = 64(8) b. 8(64) - 28 = $w$ c. 28$w$ - 64 = 8 d. 8$w$ + 28 = 64 #### Answer: (d) Correct answer : (4) 13. Zelma had$20 in her pocket. The money left with her after buying books is equal to $20 minus$3.40 times the number of books she bought. Choose the function that represents a relation between the number of books she bought and the money left with her.
 a. f($n$) = 20 - 3.40$n$ b. f($n$) = 23 - 3.40$n$ c. f($n$) = 20 + 3.40$n$ d. f($n$) = 20 - $n$

14.
Nathan purchased a trouser and the shopkeeper gave him a discount of 17%. Select a function rule to represent the price of the trouser after the discount.
 a. $f$($x$) = $x$ + 17$x$ b. $f$($x$) = $x$ - 0.17$x$ c. $f$($x$) = $x$ + 0.17$x$ d. $f$($x$) = $x$ - 17$x$

15.
Nathan & Co., organized a fund raiser for the cyclone victims. Each child ticket costs $5 and an adult ticket costs$8. Choose an equation that models the total amount collected, if the company collected $521 .  a. 5$x$ - 8$y$ = 521 b. - 5$x$ + 8$y$ = 521 c. 5$x$ + 8$y$ = 521 d. 5$x$ + $y$ = 521 #### Answer: (c) Correct answer : (3) 16. Which of the following choices represents the phrase "5 added to 4 times $x$ is equal to 25"?  a. 4$x$ - 5 = 25 b. 5 + 4$x$ = 25 c. $\frac{x}{5}$ + 5 = 25 d. 4($x$ + 5) = 25 #### Solution: 4 times x = 4x 5 added to 4x = 5 + 4x [Add 5 to 4x.] 5 added to 4 times x is equal to 25 is 5 + 4x = 25. Correct answer : (2) 17. Which of the following expressions represents a two-digit number with $x$ in its ones place and $y$ in its tens place?  a. $\mathrm{xy}$ b. $y$ + $x$ c. 10$\mathrm{y+x}$ d. 10$y$ - $x$ #### Solution: A two-digit number with x in its units place and y in its tens place has a value of 10y+x. Among the choices, choice C is a two-digit number with x in its units place and y in its tens place. Correct answer : (3) 18. A problem involves adding 6 to $x$ and then dividing the sum by 7 followed by subtracting 5 from the quotient. Which of the following is the result obtained by performing the operations described above?  a. b. c. d. #### Solution: = x + 6 The first step of the operation is, add 6 to x = x + 67 The second step of the operation is, divide the sum by 7 = x + 67 - 5 The third step of the operation is, subtract 5 from the quotient = x + 67 - 51 [Write 5 as 5 / 1.] = x + 6 - 357 [The LCD of 7 and 1 is 7.] = x - 297 [Simplify.] Correct answer : (2) 19. Which of the following expressions is the correct representation of the cost of $m$ dozens of chocolate boxes, if each chocolate box costs$24.24?
 a. 24.24$m$ b. 24.24$m$ + 12 c. 24.24(12)$m$ d. 24.24 + 12$m$

#### Solution:

= 24.24(12)
The cost of a dozen chocolate boxes = The cost of each chocolate box × 12
[1 dozen = 12.]
[Substitute the cost of each chocolate box.]

The cost of m dozens of chocolate boxes = 24.24(12)(m)

20.
Danielle is 35 years younger than Chris. If Chris is $a$ years, then what is Danielle's age?
 a. 35$a$ b. $a$ + 35 c. $\frac{a}{35}$ d. $a$ - 35

#### Solution:

Age of Chris = a years.

Danielle is 35 years younger than Chris.

So, Danielle's age is (a - 35) years.