Official Guide Explanation:
Problem Solving #62




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Solution and Metadata

Question: 62
Page: 70
Difficulty: 5 (Moderate)
Category 1: Algebra > Linear Equations-Two Unk >

Explanation: Call the three integers l, m, and s. We're given three equations:

l + m + s = 40

l = 3m

s = l - 23

If we change the middle equation to m = (1/3)l, we can substitute the latter two equations into the first equation, giving us one equation with one variable:

l + ((1/3)l) + (l - 23) = 40

2l + (1/3)l = 63

(7/3)l = 63

l = 63((3/7))

l = 9(3) = 27

Given the value of l, we can determine that s = 4 and m = 9. The product of the three integers is:

4(9)(27) = 972, choice (B).

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