# When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the num

Discussion in 'Calculator Requests' started by math_celebrity, Oct 31, 2021.

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When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number

The phrase a number means an arbitrary variable, let's call it x.
x

4 times a number means we multiply x by 4:
4x

Increased by 40 means we add 40 to 4x:
4x + 40

100 decreased by the number means we subtract x from 100:
100 - x

The phrase is the same as means equal to, so we set 4x + 40 equal to 100 - x
4x + 40 = 100 - x

Solve for x in the equation 4x + 40 = 100 - x

Step 1: Group variables:
We need to group our variables 4x and -x. To do that, we add x to both sides
4x + 40 + x = -x + 100 + x

Step 2: Cancel -x on the right side:
5x + 40 = 100

Step 3: Group constants:
We need to group our constants 40 and 100. To do that, we subtract 40 from both sides
5x + 40 - 40 = 100 - 40

Step 4: Cancel 40 on the left side:
5x = 60

Step 5: Divide each side of the equation by 5
5x/5 = 60/5
x = 12

Check our work for x = 12:
4(12) + 40 ? 100 - 12
48 + 40 ? 100 - 12
88 = 88