Question

I thought of a number. If I add 30/7 to it, then subtract 22/7 from the result, and then subtract that difference from 59/7, I get 19/7. What is my number

Answer 1

32/7

Explanation:

You want to know the number that gives a result of 19/7 if 30/7 is added to it, 22/7 is subtracted from that sum, and the difference is subtracted from 59/7.

Setup

The description of the operations can be modeled by ...

59/7 -((x +30/7) -22/7) = 19/7

Solution

We can eliminate fractions by multiplying both sides of the equation by 7.

59 -(7x +30) -22) = 19

Simplifying gives ...

59 -7x -30 +22 = 19

51 -7x = 19

32 = 7x

32/7 = x

The number is 32/7.

Check

Adding 30/7 to the number gives 32/7 +30/7 = 62/7.

Subtracting 22/7 from that gives 62/7 -22/7 = 40/7.

Subtracting that from 59/7 gives 59/7 -40/7 = 19/7, as required.

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