SAT word problems: translating a ratio into a model

When you study in more than one language or school system, a familiar mathematical idea can appear in unfamiliar wording. A useful habit for SAT Math is to label the quantities before choosing an operation. Here is an original practice example.

Worked example: which group changes?

A school has international and domestic students in the ratio 3:5. There are 120 domestic students. The school admits 40 additional international students and no other students. What is the new ratio of international to domestic students?

1. Five ratio units represent 120 domestic students, so one unit is 120 ÷ 5 = 24.
2. The original international count is 3 × 24 = 72.
3. Only the international group increases: 72 + 40 = 112. The domestic count remains 120.
4. The new ratio is 112:120. Dividing both values by 8 gives 14:15.

The fraction 14/15 expresses the same ratio. It is not a different mathematical answer. If an exercise asks for a ratio, 14:15 or “14 to 15” makes the comparison explicit; use the response format the question requests.

A genuinely incorrect approach

Adding 40 to both groups would produce 112:160 = 7:10. That calculation is internally consistent, but it describes a different event. The question admits international students only. This is why naming the changed quantity matters more than recognising a familiar formula.

Try a second example

A club's ratio of junior to senior members is 2:3. It has 45 senior members. Fifteen juniors join and no seniors leave. What is the new ratio?

A repeatable reading check

• Write the two quantities in the same order as the requested ratio.
• Mark which quantity changes and which stays fixed.
• Convert the starting ratio into actual counts before applying a change.
• Check that the final answer responds to the requested comparison.

Record whether a missed question came from interpretation, arithmetic or an unfamiliar concept. Those are useful practice categories, not a formula for a guaranteed score gain.

The SAT Math Skills Check includes more original examples with explanations. For a full scored practice experience, use College Board’s Bluebook tests; the official SAT structure distinguishes Math from Reading and Writing. If you need support translating your existing curriculum knowledge into SAT practice, explore SAT tutoring.