How to find the solution to an equation

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ACT Math › How to find the solution to an equation

Questions 1 - 10
1

A car averages miles per gallon. If gas costs per gallon, which of the following is closest to how much the gas would cost for this car to travel typical miles?

Explanation

To solve this problem you should divide the total number of miles by the miles per gallon , and then multiply by the cost of gas per gallon . This gives you , which is closest to .

2

The population of a bird species is modeled by the following equation:

,

where represents the number of years from the present. How many years will it take the population to reach 130 birds (rounded to the nearest tenth)?

20.4

280.8

38.5

23.0

12.2

Explanation

Plugging in 130 for P, the equation becomes 130 = (11/8)x + 102. Solving for x, we obtain x = 20.4 years.

3

Two cars start 25 mile apart and drive away from each other in opposite directions at speeds of 50 and 70 miles per hour. In approximately how many minutes will they be 400 miles apart?

None of the other answers

187.5

200

3.33

3.125

Explanation

The cars have a distance from each other of 25 + 120t miles, where t is the number of hours, 25 is their initial distance and 120 is 50 + 70, or their combined speeds. Solve this equation for 400:

25 + 120t = 400; 120t = 375; t = 3.125

However, the question asked for minutes, so we must multiply this by 60:

3.125 * 60 = 187.5 minutes.

4

If the expression x4 + 3cx – 2 is equal to 5 when x = **–**1, what is the value of c?

**–**2

2

1

3

Explanation

Plugging in **–**1 into the equation for x and solving for c yields **–**2.

5

Give the lines y = 0.5x+3 and y=3x-2. What is the y value of the point of intersection?

2

3

4

6

7

Explanation

In order to solve for the x value you set both equations equal to each other (0.5x+3=3x-2). This gives you the x value for the point of intersection at x=2. Plugging x=2 into either equation gives you y=4.

6

3x + 9i2 – 5x = 17

What is x?

–13

13

–4

4

–1

Explanation

i =

i2 = -1

3x + 9i2 – 5x = 17

3x + 9(–1) – 5x = 17

–2x – 9 = 17

–2x = 26

x = –13

7

If y=0.35(300 – 2y), what is the value of y to the nearest tenth?

61.8

51.2

65.0

62.3

Explanation

Distributing the 0.35 to both the 300 and **–**2y leaves y=105 – 0.7y

Adding 0.7y to both sides and dividing by 1.7 gives 61.8.

8

Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.

If Pets Plus sells 50 bird houses, what is the profit?

$500

$250

$750

$300

$625

Explanation

Let x = the number of birdhouses sold each month.

Revenue=40x

Costs=15x+750

Profit = Revenue-Costs

=40x-15x-750

=25x-750

Substituting in 50 for x gives an answer of 500, so the profit on 50 birdhouses is $500.

9

Three consecutive positive numbers have the sum of 15. What is the product of these numbers?

20

45

75

120

30

Explanation

Define the variables as x = the first number, x + 1, the second number, and x + 2 the thrid number.

The sum becomes x + x + 1 + x + 2 = 15 so 3x + 3 = 15. Subtract 3 from both sides of the equation to get 3x = 12 → 3x/3 = 12/3 → x = 4

The three numbers are 4, 5, and 6 and their product is 120.

10

If 5 + x is 5 more than 5,what is the value of 2_x_?

10

5

15

20

Explanation

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2_x_ = 10

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