# Algebraic Expressions Worksheets - Page 4

Algebraic Expressions Worksheets
• Page 4
31.
A man walks 4 km and then travels a certain distance of $t$ km by train. Choose an equation for the total distance traveled by the man, if the whole journey is 71 km.
 a. 4 + $t$ = - 71 b. - 4 + $t$ = 71 c. 4 - $t$ = 71 d. 4 + $t$ = 71

#### Solution:

Distance traveled by walk = 4 km

Distance traveled by train = t km

Total distance traveled by the man = 71 km

Equation for the total distance traveled by the man is 4 + t = 71.

32.
Which of the following is the correct choice for the phrase, "$y$ is divided by a number 36"?
 a. $\frac{36}{y}$ b. $y$ - 36 c. $\frac{y}{36}$ d. $y$ + 36

#### Solution:

y is divided by a number 36.
[In words.]

y36
[Variable expression.]

Variable expression for the word phrase is y36.

33.
Identify the variable expression for the phrase "The difference between $k$ and $\frac{1}{2}$ is equal to 3".
 a. $\frac{1}{2}$ - 2$k$ = 3 b. $k$ - $\frac{1}{2}$ = 3 c. $k$ + $\frac{1}{2}$ = 3 d. $\frac{1}{2}$$k$ = 3

#### Solution:

The difference between k and 1 / 2 is equal to 3

k - 12 = 3
[Write the equation.]

So, the variable expression for the word phrase is k - 1 / 2 = 3.

34.
Which of the following variable expressions is the correct choice to express $d$ dimes in terms of nickels?
 a. $d$ b. 2$d$ c. 10$d$ d. 5$d$

#### Solution:

1 dime = 2 nickels

d dimes = 2d nickels

So, the variable expression to express d dimes in nickels is 2d.

35.
Jeff scored 38 points more than Joe did in History. Choose the correct variable expression form representing the points obtained by Jeff. Let $x$ be the points obtained by Joe in History.
 a. $x$ + 38 b. 38$x$ c. $x$ = 38 d. $x$ - 38

#### Solution:

Points obtained by Jeff = points obtained by Joe + 38
[Jeff got 38 more points than Joe.]

= x + 38
[Replace the points obtained by Joe with the variable x.]

So, the variable expression representing the points obtained by Jeff is x + 38.

36.
Rebecca bought 4 kg of onions and 2 kg of tomatoes for $35. Which of the following choices represents the appropriate equation for the situation, if $t$ represents the cost of 1 kg of onions and $p$ represents the cost of 1 kg of tomatoes?  a. 2$p$ = 39 b. 4$t$ = 37 c. 4$t$ - 2$p$ = 39 d. 4$t$ + 2$p$ = 35 #### Solution: The cost of 1 kg of onions is t and that of tomatoes is p. Cost of 4 kg of onions = 4t. Cost of 2 kg of tomatoes = 2p. Total cost of onions and tomatoes that Rebecca bought = 4t + 2p. So the required equation is 4t + 2p = 35. [Given the total cost of onions and tomatoes that Rebecca bought is$35.]

37.
Which of the following inequalities represents the sentence "A number divided by 5 is less than or equal to 4."?
Let $y$ represent the number.
 a. $y$ ≤ 5 + 4 b. $y$ + 5 ≤ 4 c. $\frac{5}{y}$ ≤ 4 d. $\frac{y}{5}$ ≤ 4

#### Solution:

The variable expression representing the word phrase is y5 ≤ 4.

38.
Express the inequality 25$x$ > 120, as a word sentence. Let $x$ represent the number.
 a. The sum of 25 and a number is greater than 120 b. The product of 25 and a number is less than 120 c. The product of 25 and a number is greater than 120 d. The sum of 25 and a number is less than 120

#### Solution:

25x > 120
[Given inequality.]

The sentence form of the inequality is : The product of 25 and a number is greater than 120.