﻿ Algebraic Expressions Worksheets - Page 3 | Problems & Solutions

# Algebraic Expressions Worksheets - Page 3

Algebraic Expressions Worksheets
• Page 3
21.
Which of the following is the correct choice for the phrase given below?
"William has 4 dollars more than Sam"
(Let $x$ represent the money that William has and $y$ represent the money that Sam has.)
 a. $y$ = 4$x$ b. $y$ = $x$ + 4 c. $x$ = 4$y$ d. $x$ = $y$ + 4

#### Solution:

William has 4 dollars more than Sam.
[Words.]

x = y + 4
[Variable expression.]

22.
Which of the following choices represents the word phrase, "5 added to 5 times $x$ is equal to 28"?
 a. 5($x$ + 5) = 28 b. 5 + 5$x$ = 33 c. $\frac{x}{5}$ + 5 = 28 d. 5$x$ + 5 = 28

#### Solution:

5 times x = 5x

5 added to 5x = 5x + 5

5 added to 5 times x is equal to 28 is 5x + 5 = 28.

23.
A problem involves subtracting 5 from $x$ and then dividing the difference by 6 followed by adding 4 to the quotient. Which of the following is the result obtained by performing the operations described above?
 a. $\frac{x+29}{6}$ b. $\frac{x-19}{6}$ c. $\frac{x-29}{6}$ d. $\frac{x+19}{6}$

#### Solution:

The first step of the operation is, subtract 5 from x
= x - 5

The second step of the operation is, divide the difference by 6
= x-56

The third step of the operation is, add 4 to the quotient
= x-56 + 4

= x-56 + 4 / 1
= x-5+246
[Write 4 as 4 / 1.]
[The LCD of 6 and 1 is 6.]

= x+196
[Simplify.]

24.
A rope is cut into 8 equal pieces. A length of 3 ft is again cut from each of the 8 pieces. Choose the correct variable expression for the new length of each piece. Let $x$ be the length of the original rope.
 a. (8$x$ - 3) ft b. (8$x$ + 3) ft c. ($\frac{x}{8}$ - 3) ft d. ($\frac{x}{8}$ + 3) ft

#### Solution:

Length of each of the 8 pieces = x8 ft

The variable expression for the new length of each piece is (x8 - 3) ft.
[A length of 3 ft is cut from each of the 8 pieces.]

25.
Ashley's present age is 5 times Tanya's age. Identify a variable expression for the sum of their ages after 2 years. Let $x$ be the Tanya's present age.
 a. 6$x$ + 5 b. 6$x$ + 4 c. 6$x$ - 4 d. 5$x$ + 4

#### Solution:

Present age of Tanya is x.

So, Ashley's present age is 5x years.

Tanya's age after 2 years = (x + 2)

Ashley's age after 2 years = (5x + 2)

Sum of their ages after 2 years = (x + 2) + (5x + 2)
[Substitute.]

= 6x + 4
[Collect like terms and simplify.]

The variable expression for the sum of their ages after 2 years is 6x + 4.

26.
How many chocolates will each boy get if $x$ chocolates are to be shared equally among 6 boys?
 a. 6$x$ b. $\frac{x}{6}$ c. $\frac{6}{x}$ d. $x$ - 6

#### Solution:

Share of each boy = Total number of chocolatesTotal number of boys

= x6
[Substitute the values.]

27.
A snail climbs $a$ cm vertically upwards from a point on a wall then slips down $y$ cm and then climbs $z$ cm upwards again. Write the statement as a variable expression for its final position.
 a. ($\mathrm{a - y - z}$) cm b. ($\mathrm{a + y - z}$) cm c. ($\mathrm{a + y + z}$) cm d. ($\mathrm{a - y + z}$) cm

#### Solution:

Upward movement of the snail from the point = a cm
[Initial position of the snail.]

Downward movement of the snail = (a - y) cm
[Since the snail slips, y should be subtracted.]

Final position of the snail = (a - y + z) cm
[As it climbed again z should be added.]

28.
Alice's salary 4 years ago was $$y$. Now, she gets 2 times the salary and spends$2,632. Calculate her savings.
 a. $(2$y$ - 2632) b.$(2632 + 2$y$) c. $(2632 - 2$y$) d.$(2632 - $y$)

#### Solution:

Alice's present salary is $2y. [y × 2.] Alice's savings =$(2y - 2632)
[Savings = salary - amount spent.]

29.
Francis and Tim fired 13 shots each to hit a target. Each person gets $p$ points for a hit and loses $q$ points for a miss. Francis hits the mark 7 times and Tim hits the mark 5 times. Identify the variable expressions that represent their individual scores.
 a. 7$p$ - 6$q$, 5$p$ - 8$q$ b. 7$p$ - 6, 5$p$ - 8 c. 5$p$, 7$q$ d. 7$p$, 5$q$

#### Solution:

Points scored by each person = Number of hits × p - Number of missed hits × q

Number of hits that Francis missed = (13 - 7) = 6
[Subtract.]

The variable expression for the points scored by Francis is 7p - 6q.
[Step 1.]

Number of hits that Tim missed = (13 - 5) = 8
[Subtract.]

The variable expression for the points scored by Tim is 5p - 8q.
[Step 2.]

So, the variable expressions for the points scored by Francis and Tim are 7p - 6q and 5p - 8q.

30.
The number of games won by a tennis player is 7 more than the number of games he lost in a season. Represent the situation as an equation, if $w$ represents the number of games won and $l$ represents the number of games lost.
 a. $w$ = $l$ + 7 b. $l$ = $w$ + 7 c. $w$$l$ = 5 d. $w$ + $l$ = 7

#### Solution:

The number of games won by the player is 7 more than the number of games he lost.

w = l + 7
[Substitute the values.]

So, the required equation is w = l + 7.