# Math

The difference of two number is seven. when the larger number is decreased by five, then doubled, it is five more than the small number. Find the numbers.

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1. let the larger number be x
then the smaller is x-7

"the larger number is decreased by five, then doubled" ---> 2(x-5)

2(x-5) = x-7 +5
2x - 10 = x - 2
x = 8

Finish it up, and check

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2. a = larger number

b = smaller number

The difference of two number is seven mean:

a - b = 7

a - b = 7 Add b to both sides

a - b + b = 7 + b

a = 7 + b

a = b + 7

When the larger number is decreased by five, then doubled, it is five more than the small number mean:

( a - 5 ) * 2 = b + 5

Replace a = b + 7 in this equation

( b + 7 - 5 ) * 2 = b + 5

( b + 2 ) * 2 = b + 5

2 * b + 2 * 2 = b + 5

2 b + 4 = b + 5 Subtract b to both sides

2 b + 4 - b = b + 5 - b

b + 4 = 5 Subtract 4 to both sides

b + 4 - 4 = 5 - 4

b = 1

a = b + 7 = 1 + 7 = 8

a = 8

Proof:

a - b = 7

8 - 1 = 7

( a - 5 ) * 2 = b + 5

( 8 - 5 ) * 2 = 1 + 5

3 * 2 = 6

6 = 6

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