Official Guide Explanation:
Problem Solving #59




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Solution and Metadata

Question: 59
Page: 160
Difficulty: 5 (Moderate)
Category 1: Word Problems > Other >
Category 2: Algebra > Linear Equations-One Unk >

Explanation: First, set up an equation for the amount of money that Harry is paid. Use h for hours. For the first 30 hours, he earns x per hour, for a total of:


For additional hours, he earns 1.5x per hour. If he works a total of h hours, the number of additional hours he works is h - 30, so the additional income is:

(h - 30)(1.5x)

That's a total of 30x + (h - 30)(1.5x)

Using the same principle, if we call James's hours j, James's income is:

40x + (j - 40)(2x)

We know that James worked 41 hours, or j = 41, so James's income is:

40x + 1(2x) = 42x

Since Harry's income is equal to James's income, we can solve for h:

30x + (h - 30)(1.5x) = 42x

(h - 30)(1.5x) = 12x

(h - 30) = ((12x)/(1.5x))

h - 30 = 8x

h = 38, choice (D).

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