Official Guide Explanation:
Problem Solving #100

Background

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Solution and Metadata

Question: 100
Page: 166
Difficulty: 4 (Moderately Easy)
Category 1: Algebra > Linear Equations-One Unk >

Explanation: Plugging in 290 for T is simple enough; the challenge in this question is efficiently handling the calculation. Here's a useful approach:

290 = (5/9)(K - 32)

290((9/5)) = K - 32

Now, divide 290 by 5. That can be done in your head: just double 290 (result: 580) and divide by 10 (result: 58).

58(9) + 32 = K

The product of 58 and 9 is trickier, but still doable with mental math tricks. 58(9) is really 58(10 - 1), so multiply 58 by 10 (result: 580) and subtract 58 (result: 522). Add 32, and you have your answer: 522 + 32 = 554. It may look like a lot of steps, but it's faster and more error - proof than long division and pencil - and - paper multiplication.

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