Percent & Ratio Word Problems: A No-Panic Guide
Turn confusing word problems into simple equations using the 'is/of' translation method.
Why Students Panic
Percent and ratio word problems aren't hard mathematically — they're hard linguistically. The SAT writes them in ways that are deliberately confusing. The fix? Translate English into math.
The Translation Table
| English | Math |
|---|---|
| is | = |
| of | × |
| what | x |
| percent | ÷ 100 |
| more than | + |
| less than | − |
Example
"What is 30% of 250?" \(x = 0.30 \times 250 = 75\)
"15 is what percent of 60?" \(15 = \frac{x}{100} \times 60\) → \(x = 25\)
Ratio Problems: The Multiplier Method
If the ratio of boys to girls is 3:5 and there are 40 students total: 1. Parts = 3 + 5 = 8 2. Multiplier = 40 ÷ 8 = 5 3. Boys = 3 × 5 = 15, Girls = 5 × 5 = 25
Percent Change Formula
Always divide by the original, not the new value. This is the #1 mistake.
Practice Problem
A store raises prices by 20%, then offers a 20% discount. Is the final price the same as the original? (Spoiler: No — it's 96% of the original. Work through it to see why.)