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.)

(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 |

[Words.]

[Variable expression.]

Correct answer : (4)

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 |

5 added to 5

[Add 5 to 5

5 added to 5 times

Correct answer : (4)

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. | $\frac{x+19}{6}$ |

=

The second step of the operation is, divide the difference by 6

=

The third step of the operation is, add 4 to the quotient

=

=

=

[Write 4 as

[The LCD of 6 and 1 is 6.]

=

[Simplify.]

Correct answer : (4)

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 |

The variable expression for the new length of each piece is (

[A length of 3 ft is cut from each of the 8 pieces.]

Correct answer : (3)

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 |

So, Ashley's present age is 5

Tanya's age after 2 years = (

Ashley's age after 2 years = (5

Sum of their ages after 2 years = (

[Substitute.]

= 6

[Collect like terms and simplify.]

The variable expression for the sum of their ages after 2 years is 6

Correct answer : (2)

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 |

=

[Substitute the values.]

Correct answer : (2)

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. | |||

b. | |||

c. | |||

d. |

[Initial position of the snail.]

Downward movement of the snail = (

[Since the snail slips,

Final position of the snail = (

[As it climbed again

Correct answer : (4)

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 - $y$) |

[

Alice's savings = $(2

[Savings = salary - amount spent.]

Correct answer : (1)

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$q$ |

Number of hits that Francis missed = (13 - 7) = 6

[Subtract.]

The variable expression for the points scored by Francis is 7

[Step 1.]

Number of hits that Tim missed = (13 - 5) = 8

[Subtract.]

The variable expression for the points scored by Tim is 5

[Step 2.]

So, the variable expressions for the points scored by Francis and Tim are 7

Correct answer : (1)

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 |

[Substitute the values.]

So, the required equation is

Correct answer : (1)