To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

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.


Correct answer : (4)
 32.  
Which of the following is the correct choice for the phrase, "y is divided by a number 36"?
a.
36y
b.
y - 36
c.
y36
d.
y + 36


Solution:

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

y36
[Variable expression.]

Variable expression for the word phrase is y36.


Correct answer : (3)
 33.  
Identify the variable expression for the phrase "The difference between k and 1 2 is equal to 3".
a.
1 2 - 2k = 3
b.
k - 1 2 = 3
c.
k + 1 2 = 3
d.
1 2k = 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.


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.
2d
c.
10d
d.
5d


Solution:

1 dime = 2 nickels

d dimes = 2d nickels

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


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.
38x
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.


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.
2p = 39
b.
4t = 37
c.
4t - 2p = 39
d.
4t + 2p = 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.]


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.
a.
y ≤ 5 + 4
b.
y + 5 ≤ 4
c.
5y ≤ 4
d.
y5 ≤ 4


Solution:

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


Correct answer : (4)
 38.  
Express the inequality 25x > 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.


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.
4t = 130
b.
5b + 4t = 130
c.
5b - 4t = 130
d.
5b = 130


Solution:

= 5 × b = 5b
The cost of 5 belts = number of belts × cost of one belt
[Substitute the values.]

= 4 × t = 4t
The cost of 4 ties = number of ties × cost of one tie
[Substitute the values.]

= 5b + 4t
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, 5b + 4t = 130

So, the correct variable expression for the word phrase is 5b + 4t = 130.


Correct answer : (2)

*AP and SAT are registered trademarks of the College Board.