The ratio of adults to students on a class field trip is 2 to 5. If there are 12 more students than adults, which proportion and solution represent this situation?
Question
The ratio of adults to students on a class field trip is 2 to 5. If there are 12 more students than adults, which proportion and solution represent this situation?
Solution
Let's denote the number of adults as A and the number of students as S.
From the problem, we know two things:
- The ratio of adults to students is 2 to 5. This can be written as A/S = 2/5.
- There are 12 more students than adults. This can be written as S = A + 12.
We can solve this system of equations step by step:
Step 1: Substitute the second equation into the first to get A/(A + 12) = 2/5.
Step 2: Cross-multiply to get rid of the fraction: 5A = 2(A + 12).
Step 3: Distribute the 2 on the right side: 5A = 2A + 24.
Step 4: Subtract 2A from both sides: 3A = 24.
Step 5: Divide by 3: A = 8.
So there are 8 adults.
Substitute A = 8 into the second equation: S = 8 + 12 = 20.
So there are 20 students.
Therefore, the proportion that represents this situation is 8 adults to 20 students, or 8:20, which simplifies to 2:5, confirming our solution.
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