Question

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

Answer 1

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.