ACT Prep Linear Equations
1.
The balance in Joan’s savings account tripled during the year. Joan then withdrew $500, and the resulting
balance was $100. What was the balance in the account before it tripled?
A.
B.
C.
D.
E.
2.
$200
$300
$400
$500
$600
For what value of x is the equation 2(x – 6) + x = 18 ?
F. 15
G. 10
H. 8
J.
4
K. 2
3.
An earring manufacturing company has fixed costs of $10,000 per month and production costs of $0.60 for
each pair of earrings it makes. If the company produces x pairs of earrings in a month, which of the
following expressions represents the total of the company’s monthly costs?
A.
B.
C.
D.
E.
4.
$10,000x
$10,000 + x
$10,000x + $0.60
$10,000 + $0.60x
($10,000 + $0.60)x
In the formula d = rt, d represents distance in miles, r represents average speed in miles per hour, and t
represents time in hours. What is an automobile’s average speed, in miles per hour, if it travels 60 miles in
1 12 hours?
F.
30
G. 40
H. 60
J.
90
K. 120
5.
For what value of a is x = 3 a solution to the equation x + 3 = ax + 9 ?
A. 1.5
B. 1
C. -1
D. -1.5
E. -3
6.
Due to inflation, a car that formerly sold for $15,000 now sells for 10% more. Which of the following
calculations gives the current cost, in dollars, of the car?
F.
G.
H.
J.
K.
7.
$15,000 + 10
$15,000 + $15,000(0.01)
$15,000 + $15,000(0.10)
$15,000 + $15,000(10)
$15,000(0.10)
A truck sprang a leak at the bottom of its radiator, which held 480 ounces of fluid when it started to leak,
and started losing radiator fluid at a constant rate of 4 ounces per minute. Suppose that the radiator
continued to leak at this constant rate and that the truck, traveling at 35 piles per hour, could continue
traveling at this rate until its radiator was completely empty. In how many miles would the radiator be
empty?
F. 13.7
G. 17.5
H. 35.0
J.
70.0
K. 120.0
8.
To purchase a car that costs $3,500, a buyer has to pay, in addition, $250 for insurance and $250 for taxes
and fees. If the buyer has $1,800 saved for a car, what amount must be borrowed to be able to buy the car
and pay these expenses?
A.
B.
C.
D.
E.
$1,200
$1,700
$2,200
$4,000
$5,800
9.
x
What is the value of x if 2
 5x
=1?
A. 107
B. 107
C. 7
D. 8
E. 10
10. Michelle went shopping for some clothes and found a pair of slacks that cost twice as much as a shirt that
she liked. If the total, before tax, for the pair of slacks and the shirt was $22.50, how much was the shirt,
before tax?
A.
B.
C.
D.
E.
$ 5.62
$ 7.50
$10.00
$11.25
$15.00
11. The equation
2
3
x  12  12 x  23 has only 1 solution for x. What is this solution?
F. 1
G. 76
H. 73
J. 3
K. 7
12. If 3x – 4 = -2(x – 3), the x = ?
F.
G.
H.
J.
K.
1/5
2/5
1
2
10
13. If 18 – 3(5 – x) = x – 7, then x = ?
F.
G.
H.
J.
K.
-8
-5
-1
5
10
14. If 2x – 3 = 12, then x = ?
A. 2.0
B. 4.5
C. 7.5
D. 9.0
E. 15.0
15. For each day on your newspaper route you receive $10.00 plus a fixed amount for each newspaper you
deliver. Currently you are earning $18.00 per day for delivery of 80 newspapers. Today you are assigned
to deliver 20 additional newspapers per day. What will be your new daily earnings?
A.
B.
C.
D.
E.
$10.00
$18.20
$19.00
$20.00
$22.50
16. Miguel is going on a business trip to Toronto, Canada. He is exchanging some U.S. dollars for Canadian
dollars. If the exchange rate between the number of U.S. dollars (u) and the number of Canadian dollars ©
is expressed in the equation 1.3 u = c, approximately how many Canadian dollars will Miguel receive in
exchange for 845 U.S. dollars?
A.
B.
C.
D.
E.
650
850
920
1,100
1,540
17. If 6 – 2(x – 3) = 8, then x = ?
A.
B.
C.
D.
E.
2
1
2
5
2
-4
-10
18. The July reading of Mr. Corelli’s electric meter, in kilowatt-hours (kwh), was 6,278 hwh. On August 1, his
electric meter registered 6,328 kwh but was not read by the utility company. Instead, the company
estimated that Mr. Corelli had used 60 kwh of electricity during July. If each kwh costs $0.10, what, if any,
was the overcharge on Mr. Corelli’s bill for July, which would be credited to his next bill?
A.
B.
C.
D.
E.
$1
$3
$6
$7
There was no overcharge on the bill.
19. If 7 + 3x = 22, then 2x = ?
F.
G.
H.
J.
K.
5
10
12
14
58
3
20. John Jones has decided to go into the business of producing and selling boats. In order to begin this
venture, he must invest $10 million in a boat production plant. The cost to produce each boat will be
$7,000, and the selling price will be $20,000. Accounting for the cost of the production plant, which of the
following expressions represents the profit, in dollars, that John will realize when x boats are produced and
sold?
A.
13,000x – 10,000,000
B.
27,000x – 10,000,000
C. 9,973,000x
D.
20,000x
E.
13,000x
21. A flight instructor charges $50 per lesson, plus an additional fee for the use of his plane. The charge for the
use of the plane varies directly with the square root of the time the plane is used. If a lesson plus 16
minutes of plane usage costs $90, what is the total amount charged for a lesson having 36 minutes of plane
usage?
A.
B.
C.
D.
E.
$185
$150
$135
$110
$ 60
22. If .05y + 7.1 = y – 8.1, then y = ?
F. -380
G. -38
H.
16
J.
25
K.
38
23. What is the smallest positive whole number that is divisible with zero remainder by both 15 and 12?
F.
G.
H.
J.
K.
3
20
30
60
180
24. For all real numbers b and c, such that the product of c and 3 is b, which of the following expressions
represents the sum of c and 3 in terms of b?
A. b + 3
B. 3b + 3
C. 3(b + 3)
D. b 3 3
E.
25. If
b
3
+3
2 x = 8 then x2 = ?
F.
4
G. 8
H. 16
J. 32
K. 64
26. The cost of electricity at the local utility company is 10 cents per kilowatt-hour for the first 100 kilowatthours used in a month and 7 cents per kilowatt-hour for each additional kilowatt-hour used. What is the
cost for 500 kilowatt-hours used in 1 month?
F.
G.
H.
J.
K.
$28.00
$35.00
$38.00
$50.00
$85.00