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.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    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
     

Share This Page