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 |

Distance traveled by train =

Total distance traveled by the man = 71 km

Equation for the total distance traveled by the man is 4 +

Correct answer : (4)

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 |

[In words.]

[Variable expression.]

Variable expression for the word phrase is

Correct answer : (3)

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 |

[Write the equation.]

So, the variable expression for the word phrase is

Correct answer : (2)

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$d$ |

So, the variable expression to express

Correct answer : (2)

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 |

[Jeff got 38 more points than Joe.]

=

So, the variable expression representing the points obtained by Jeff is

Correct answer : (1)

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 |

Cost of 4 kg of onions = 4

Cost of 2 kg of tomatoes = 2

Total cost of onions and tomatoes that Rebecca bought = 4

So the required equation is 4

[Given the total cost of onions and tomatoes that Rebecca bought is $35.]

Correct answer : (4)

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.

Let $y$ represent the number.

a. | $y$ ≤ 5 + 4 | ||

b. | $y$ + 5 ≤ 4 | ||

c. | $\frac{5}{y}$ ≤ 4 | ||

d. | $\frac{y}{5}$ ≤ 4 |

Correct answer : (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 |

[Given inequality.]

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

Correct answer : (3)

39.

Select the correct equation for the statement, "Cost of 5 belts and 4 ties is $130". Let $b$ be the cost of one belt and $t$ be the cost of one tie.

a. | 4$t$ = 130 | ||

b. | 5$b$ + 4$t$ = 130 | ||

c. | 5$b$ - 4$t$ = 130 | ||

d. | 5$b$ = 130 |

The cost of 5 belts = number of belts × cost of one belt

[Substitute the values.]

= 4 ×

The cost of 4 ties = number of ties × cost of one tie

[Substitute the values.]

= 5

Cost of 5 belts and 4 ties = cost of 5 belts + cost of 4 ties

[Substitute the costs.]

Cost of 5 belts and 4 ties = $130

[Given.]

So, 5

So, the correct variable expression for the word phrase is 5

Correct answer : (2)