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Two different triples of numbers are each in arithmetic progression, and the sum of the three terms in each triple is 15. The common difference of the first triple exceeds that of the second by 1. Also, the ratio of the product of the three terms in the first triple to the product of the three terms in the second triple is 7:8. What is the ratio of the smallest term in the first triple to the smallest term in the second triple?

1. 3/4 or 11/12
2. 2/3 or 1/2
3. 2/3 or 3/4
4. None of these

Correct answer: 3/4 or 11/12

Solution

Sum 15 means middle term 5, so terms are 5-d,5,5+d with product 125-5d^2. The ratio (25-d1^2)/(25-d2^2)=7/8 with d1=d2+1 gives (d2,d1)=(1,2) or (-17,-16). Smallest-term ratios are 3/4 and 11/12.

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