RATIOS, PROPORTIONS, AND RATES
30 . Finding the Original Whole
To find the original whole before a percent increase or decrease, set up
an equation. Think of the result of a 15 percent increase over x as 1.15x.
Example: After a 5 percent increase, the population was 59,346. What
was the population before the increase?
Setup: 1.05x = 59,346
31 . Combined Percent Increase and Decrease
To determine the combined effect of multiple percent increases and/or
decreases, start with 100 and see what happens.
Example: A price went up 10 percent one year, and the new price
went up 20 percent the next year. What was the combined
percent increase?
Setup: First year: 100 + (10 percent of 100) = 110. Second year: 110
+ (20 percent of 110) = 132. That’s a combined 32 percent
increase.
32 . Setting Up a Ratio
To find a ratio, put the number associated with the word of on top and the
quantity associated with the word to on the bottom and reduce. The ratio
of 20 oranges to 12 apples is which reduces to
33 . Part-to-Part Ratios and Part-to-Whole Ratios
If the parts add up to the whole, a part-to-part ratio can be turned into two
part-to-whole ratios by putting each number in the original ratio over the
