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A number is increased by 60% after first subtracting 22, making it half the original size. What was the original number?

User Imdad
by
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1 Answer

5 votes

Answer:

32

Explanation:

Let x be "A number."

" . . . first subtracting 22 . . ." suggests the first thing that should be done:

x-22

" increased by 60%" means increse the number from above (x-22) by a factor of (1 + 0.60). This takes the number (x-22) and adds 60% (0.60) to it.

(x-22)*(1.6) = (1.6x - 35.2)

" . . . making it half the original size." half the original size is:

(1/2)x

Now put the two expressions together:

(1.6x - 35.2) = (1/2)x

1.6x - 35.2 = 0.5x

1.1x = 35.2

x = 32

"A number" is 32.

Check the answer:

1) Subtract 22: 32-22 = 10

2) Increase by 60%: 16

Is 16 half the original number of 32? YES

User Frederick Behrends
by
6.1k points
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