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12 July, 09:25

Richard is seven years older than Lilia. In ten years, the sum of their ages will be 51. How old is Richard now?

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  1. 12 July, 09:45
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    Answer

    19

    Step-by-step explanation:

    For this example, R = Richard and L = Lilia. You'll need to set up a system of equations with the information that the problem gives you.

    R = L + 7

    (R+10) + (L+10) = 51

    Use the substitution method so that you only have one variable in the equation. The first equation tells you that R is the same as L+7, so put L+7 instead of R everywhere you see R in the second equation.

    [ (L+7) + 10) + (L+10) = 51

    L + 7 + 10 + L + 10 = 51

    Combine like terms.

    2L + 27 = 51

    Isolate the variable by subtracting first, then dividing.

    2L + 27 - 27 = 51 - 27

    2L = 24

    2L/2 = 24/2

    L = 12

    You just solved for L (Lilia's age). Don't forget that you're trying to find R (Richard's age), so plug your L number into the first equation.

    R = L + 7

    R = 12 + 7

    R = 19

    Check your answer by plugging your solutions (R and L) into the second equation and see if it's true.

    (R+10) + (L+10) = 51

    (19+10) + (12+10) = 51

    29 + 22 = 51

    51 = 51 is true.
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