Finding Original Given New Amount Changed and Percent

Let’s take a look at this word problem here. If Stephen has grown 10 percent in two years and he is now 5 foot 6, how tall was he two years ago? Now, a lot of people look at this problem and just take 10 percent away from 5 foot 6.

Then call that the answer, but that is not the correct answer. To give the correct answer you have to take 10 percent away from the original height rather than 10 percent from the current height. That means our equation has to look like this.

The current height is equal to the original height plus 10 percent, times the original height. We’re looking for the original height. To solve for the original height, we have to combine these two terms. We’re going to need to convert this percentage to a decimal.

We can rewrite this CH equals OH plus 0.1OH. Now, we can add these two together. This is 1O H, this is 0.1OH. We can rewrite this as 1.1O H. Now, to solve for OH, all we have to do is divide both sides of the equation by 1.1.

This one point one would cancel, and what we’re left with is the original height is equal to the current height, divided by 1.1. Now, the current height is given to us in feet and inches. We need to convert this to inches before we plug it here. 5 feet 6 inches is equal to 5 times 12, plus 6.

This is 5 times 12 is 60, plus 6, is 66. Stephen is 66 inches currently, and we need to divide it by 1.1 to get his original height. 66 over 1.1. Now, 66 divided by 1.1 is equal to 60. Stephen’s original height is 60 inches. We had it given to us in feet and inches, so we need to convert it back. 60 inches over 12 inches per foot gives us 5 feet with no remainder. Steven’s original height was five feet.