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

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 = 4x
b.
y = x + 4
c.
x = 4y
d.
x = y + 4


Solution:

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

x = y + 4
[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 + 5x = 33
c.
x5 + 5 = 28
d.
5x + 5 = 28


Solution:

5 times x = 5x

5 added to 5x = 5x + 5
[Add 5 to 5x.]

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


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.
x+296
b.
x-196
c.
x-296
d.
x+196


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.]


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.
(8x - 3) ft
b.
(8x + 3) ft
c.
(x8 - 3) ft
d.
(x8 + 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.]


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.
6x + 5
b.
6x + 4
c.
6x - 4
d.
5x + 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.


Correct answer : (2)
 26.  
How many chocolates will each boy get if x chocolates are to be shared equally among 6 boys?
a.
6x
b.
x6
c.
6x
d.
x - 6


Solution:

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

= x6
[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.
(a - y - z) cm
b.
(a + y - z) cm
c.
(a + y + z) cm
d.
(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.]


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.
$(2y - 2632)
b.
$(2632 + 2y)
c.
$(2632 - 2y)
d.
$(2632 - y)


Solution:

Alice's present salary is $2y.
[y × 2.]

Alice's savings = $(2y - 2632)
[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.
7p - 6q, 5p - 8q
b.
7p - 6, 5p - 8
c.
5p, 7q
d.
7p, 5q


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.


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.
wl = 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.


Correct answer : (1)

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