Elementary Algebra Age Question

Question

Michael is 6 years older than Richard. 11 years ago, Michael was 4 times as old as Richard was then. How old are they now?

Answer 1

M: Michael's age now

R: Richard's age now

Michael is 6 years older than Richard:

M = R + 6

11 years ago, Michael was 4 times as old as Richard was then:

M - 11 = 4 (R - 11)

Replacing M, from the first equation into the second equation:

(R + 6) - 11 = 4 (R - 11)

R + 6 - 11 = 4R - 44

R - 5 = 4R - 44

R - 4R = -44 + 5

-3R = -39

R = -39 / -3

R = 13

Replacing R, in the first first equation:

M = R + 6

M = 13 + 6

M = 19

Michael is 19 and Richard is 13 now.