Linear / Rational / Variable Equations
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ACT Math › Linear / Rational / Variable Equations
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.
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.
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.
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.
The population of a bird species is modeled by the following equation:
where 
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.
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?
Explanation
Let 
Revenue:
Costs:
Profits = 
So the equation to solve becomes
So to make a profit of $750, 52 teddy bears must be sold.
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.
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.
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
The population of a bird species is modeled by the following equation:
where
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.