ACT Math › Equations / Inequalities
If 5 + x is 5 more than 5,what is the value of 2_x_?
10
5
15
20
5 more than 5 = 10
5 + x = 10
Subtract 5 from each side of the equation: x = 5 → 2_x_ = 10
Three consecutive even numbers add to 42. What is the middle number?
Let = 1st even number,
= 2nd even number, and
= 3rd even number.
Then the equation to solve becomes .
Thus , so the middle number is 14.
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
Plugging in 130 for P, the equation becomes 130 = (11/8)x + 102. Solving for x, we obtain x = 20.4 years.
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
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.
If the expression x4 + 3cx – 2 is equal to 5 when x = **–**1, what is the value of c?
**–**2
2
1
3
Plugging in **–**1 into the equation for x and solving for c yields **–**2.
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
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.
3x + 9i2 – 5x = 17
What is x?
–13
13
–4
4
–1
i =
i2 = -1
3x + 9i2 – 5x = 17
3x + 9(–1) – 5x = 17
–2x – 9 = 17
–2x = 26
x = –13
If y=0.35(300 – 2y), what is the value of y to the nearest tenth?
61.8
51.2
65.0
62.3
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.
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?
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
.
The Teddy Bear Parade makes teddy bears. Their monthly fixed costs are $550. It costs $25 to make each bear and they sell for $50 each.
To make a profit of $750, how many teddy bears must be sold?
Let = number of teddy bears sold.
Revenue:
Costs:
Profits = or
So the equation to solve becomes
So to make a profit of $750, 52 teddy bears must be sold.