ACT Math : Linear / Rational / Variable Equations
Study concepts, example questions & explanations for ACT Math
All ACT Math Resources
Example Questions
Example Question #41 : How To Find The Solution To An Equation
How much pure water must be added to 2 gallons of 90% pure cleaning solution to yield a 30% pure cleaning solution?
Let pure water be 0% and pure solution be 100%.
So the general equation to solve is:
So the equation to solve becomes
Solving shows that we need to add 4 gallons of pure water to 2 gallons of 90% pure cleaning solution to get a 30% pure solution.
Example Question #101 : Linear / Rational / Variable Equations
Susan got a new piggy bank and counted the change she put into it. She had one more nickel than dimes and two fewer quarters than nickles. The value of her change was $1.40. How many total coins did she have?
Let 
The general equation to use is:
So the equation to solve becomes
Thus, solving the equation shows that she had five nickels, four dimes, and three quarters giving a total of 12 coins.
Example Question #224 : Algebra
How much pure water should be added to 
Pure water is 0% and pure solution is 100%
So the equation to solve becomes
So we need to add 
Example Question #102 : Linear / Rational / Variable Equations
Luke purchased a tractor for $1200. The value of the tractor decreases by 25 percent each year. The value, 
In how many years from the date of purchase will the value of the tractor be $675?
3
2
1
4
5
2
We are looking for the value of t that gives $675 as the result when plugged in V (t ). While there are many ways to do this, one of the fastest is to plug in the answer choices as values of t .
When we plug t = 1 into V (t ), we get V (1) = 1200(0.75)1 = 1000(0.75) = $900, which is incorrect.
When we plug t = 2 into V (t ), we get V (2) = 1200(0.75)2 = $675, so this is our solution.
The value of the tractor will be $675 after 2 years.
Finally, we can see that if t = 3, 4, or 5, the resulting values of the V (t ) are all incorrect.
Example Question #103 : Linear / Rational / Variable Equations
Solve for 
First combine like terms. In this case, 4x and 9x can be added together:
13x + 13 = 0
Subtract 13 from both sides:
13x = -13
Divide both sides by 13 to isolate x:
x = -13/13
x = -1
Example Question #51 : Linear / Rational / Variable Equations
Ben is walking three dogs that weigh an average of 75 pounds each. Ben begins to walk a fourth dog, and the average weight of the dogs decreases to 70 pounds. What is the weight in pounds of the fourth dog?
The total weight of the first three dogs is 225 pounds. This amount, plus the weight of the fourth dog, divided by total number of dogs, is the new average weight:
Example Question #52 : Linear / Rational / Variable Equations
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.
What is the monthly break-even point at Pets Plus?
Let 
The break-even point is where the revenue is the same as the costs:
Solve for 
Therefore, Pets Plus must sell 30 bird houses to break-even.
Example Question #53 : Linear / Rational / Variable Equations
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?
Let 
Substituting in 50 for 
Example Question #54 : Linear / Rational / Variable Equations
George is three times older than Joey. The sum of their ages is 16. What is the product of their ages?
Let 
Then the equation to solve becomes 
Therefore, Joey is 4 years old and George is 12 years old, so the product of their ages is 48.
Example Question #55 : Linear / Rational / Variable Equations
Three consecutive even numbers add to 42. What is the middle number?
Let 
Then the equation to solve becomes 
Thus 
Certified Tutor
All ACT Math Resources
