SAT tutoring in Abu Dhabi: equivalent ratios after a group changes
Simplifying a ratio preserves its relationship when you divide both quantities by the same nonzero number. A ratio written with larger numbers is not automatically wrong. If the question asks for simplest form, that adds a formatting requirement to the mathematical relationship.
Original teaching problem
A school has 240 students, with a boys:girls ratio of 3:5. Twelve additional boys enrol, and the number of girls stays unchanged. What is the new boys:girls ratio in simplest whole-number form?
This is an original exercise, not an official SAT question or a description of a particular school in Abu Dhabi.
Find the actual counts first
The eight ratio parts represent 240 students, so each part represents 30 students. Initially, there are 3 × 30 = 90 boys and 5 × 30 = 150 girls.
After enrolment, there are 102 boys and 150 girls. The new ratio is therefore 102:150. Dividing both sides by 6 gives 17:25, its simplest whole-number form.
Distinguish equivalence from a changed population
The ratios 102:150, 34:50 and 17:25 are equivalent. They all describe the same boys-to-girls relationship. Only 17:25 satisfies this question’s request for simplest form, because 17 and 25 share no common factor greater than 1.
By contrast, the original ratio 3:5 is not equivalent to the new ratio. The boys increased while the girls did not. As a numerical check, 90/150 = 0.60 and 102/150 = 0.68, so the boys-to-girls ratio increased as expected.
If both populations had doubled, their ratio would have stayed 3:5. Adding a fixed number to one population is different from multiplying both populations by the same factor.
Answer the relationship actually requested
The new total is 252 students. If a different question asked for the fraction of all students who are boys, the answer would be 102/252 = 17/42. The denominator changes because the comparison is now boys to total, not boys to girls.
Ratios and proportions are part of the SAT’s Problem-Solving and Data Analysis domain. Review the comparison named in each problem instead of attaching a fixed score penalty to a mistake.
For further practice, try the free Math Skills Check. See online SAT tutoring for Abu Dhabi students if you want to discuss your setup and checking method.