SAT ratio and percentage practice: what can the information establish?
In a word problem, use the information given and stop where it stops. A module label does not change a correct mathematical method. This original exercise combines a part-to-part ratio with a percentage change.
The espresso problem
On Monday, a café sold 120 drinks, all espresso or cappuccino. The ratio of espresso to cappuccino was 3:5. On Tuesday, the number of espressos sold was 20% greater than Monday’s. How many espressos were sold on Tuesday?
- The ratio has 3 + 5 = 8 parts in total.
- Each part represents 120 ÷ 8 = 15 drinks.
- Monday’s espresso count is 3 × 15 = 45.
- Tuesday’s count is 45 × 1.20 = 54 espressos.
This is a correct approach. Adding 20% of 45, or 9 drinks, gives the same result. There is no reason to reject 54 because the exercise might appear in one module rather than another.
What cannot be determined?
The prompt gives no Tuesday cappuccino count. Therefore it does not establish Tuesday’s total drinks or espresso-to-cappuccino ratio.
Tuesday could consist of 54 espressos and 75 cappuccinos, for a total of 129 drinks. It could instead consist of 54 espressos and 90 cappuccinos, for a total of 144. These are two complete possible sales totals, and both fit the stated espresso information. Assuming Tuesday’s total remained 120 would add a condition that was never given.
Turn the distinction into practice
Label whether a ratio compares two parts or a part with the whole. Apply a percentage to the quantity it names. Finally, check whether the requested answer requires any missing information.
Use the SAT Math Skills Check for more original exercises and official Bluebook practice for a scored full-format baseline. SAT scoring does not attach a fixed number of points to this example or promise a weekly gain.
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