Solving equations for a variable - Middle Level

James is filling his new swimming pool with water. For his first try, he filled 10 gallons less than half of the maximum volume that the pool can hold. The equation below represents this relationship:
t= ½ v – 10
Where t is the weight of his first set and v is the maximum volume that the pool can hold. If the volume of his first try is 115 gallons, what is the maximum gallons that he can fill?

a. 65.7 gallons
b. 82.5 gallons
c. 175.0 gallons
d. 250.0 gallons

Answer : d

Explanation :
Lets try to solve the equation by asking : what is it we are trying to find out?
We realize that this linear question is asking us to find out what the maximum volume is, which means to find what v is. This means that we are trying to solve this equation for the variable v.
In order to do that we have to plug in the knowns into the equation to be able to find the unkown.
We know that:
t = 115 so lets start:
115 = ½ v - 10
now we have to isolate the variable by grouping the numbers on one side of the equation.
In order to do that we must add 10 to each side so here goes:
115 + 10 = ½ v – 10 + 10
The 10’s cancel on the right side and we are left with :
125 = ½ v
In order to solve for v we must get rid of the ½. To do that we must multiply each side of the equation by 2, so lets try it:
125 (2) = ½ (2) v
Notice that the 2's cancel each other out on the right side and we are left with:
250 = v
We have now solved for v.
To check our work lets substitute the value we found for v in the original equation to find out if the right side of the equation equals the left side.
115 = ½ (250) – 10
115 = 125 – 10
115 = 115 It checks ok
For additional information about solving linear equation try this webpage:
Solving Linear Equations

©Copyright 2007.Najwa S. Hirn. All rights reserved.