Four years less than twice Mark’s age is equal to twice Russ’s age 4 years ago. If Russ’s age is an integer greater than

VJesus12 wrote: ↑

Sat Jan 23, 2021 2:26 pm

Four years less than twice Mark’s age is equal to twice Russ’s age 4 years ago. If Russ’s age is an integer greater than 22, then which of the following could be the sum of their ages?

A. 36
B. 38
C. 45
D. 47
E. 54

Answer: E

Solution:

We can let m = Mark’s current age and r = Russ’s current age and create the equation:

2m - 4 = 2(r - 4)

2m - 4 = 2r - 8

m - 2 = r - 4

m = r - 2

We see that Russ is two years older than Mark. Since Russ’ age is an integer greater than 22, Mark’s age is an integer greater than 20. Therefore, the sum of their ages is greater than 42. Moreover, since the difference between their ages is 2, their ages are either both even or both odd. In either case, the sum of their ages will be even. There is only one answer choice which is greater than 42 and is even, and that is answer choice E.

Answer: E