The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is :__________?
Correct answer: B. 30
- A. 20
- B. 30
- C. 48
- D. 58
Explanation
Let the first two numbers be 2k and 3k, and the last two be 5m and 8m. Since 3k = 5m, use m = 3t and k = 5t, giving the numbers 10t, 15t and 24t; their sum is 49t = 98, so t = 2 and the second number is 30. The likely wrong choice is 20, which comes from using only the first ratio and overlooking the second ratio.
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Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.
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