Mary is 4 years younger than 4 times Chris' age. If Mary's age 3 years ago was equal to what Chris' age will be in 9 years, how old is each person?

Answer 1

Let m = Mary's age and c = Chris's age, then 4 times Chris's age is 4c and since Mary is 4 years younger than that, if I add 4 years to Mary's age I'll be the same as 4c. That means m + 4 = 4c

Mary's age tree years ago would be m - 3. Chris's age in 9 years is c + 9. So m - 3 = c + 9 or simplifying this by adding 3 to both sides of the equation: m = c + 12

The two equations are:

m + 4 = 4c

m = c + 12

Since m is equal to c + 12, I can interchange them, so wherever there is an m in the first equation, I'm going to substitute in "c + 12" so:

(c + 12) + 4 = 4c

c + 16 = 4c

16 = 3c

c = 16/3 = 5 1/3

Plugging that into m = c + 12, m = 5 1/3 + 12 = 17 1/3

So Chris is 5 1/3 years (5 years, 4 months) and Mary is 17 1/3 (17 and 4 months)