Substituion and elimination

Question

Armando is 6 years older than María. In 4 years the sum of their ages will be 78 . How old is Armando now?

Answer 1

Let A = Armando's age NOW.

Let M = Maria's age NOW.

Then in 4 years:

Armando will be A + 4

Maria will be M + 4.

Today Armando is 6 years older than Maria.

A = M + 6

In 4 years the sum of their ages is 78:

A + 4 + M + 4 = 78

A + M + 8 = 78

A + M = 70

Since we know A = M + 6, substitute that value for A into the previous equation:

(M + 6 ) + M = 70

2M = 64

M = 32 which is Maria's age today.

A = 32 + 6 = 38 (Armando is 6 years older than Maria today).

In four years Maria will be 36 and Armando will be 42. The sum of those ages is indeed 78.

This is just one of a few different ways to determine Armando's age today (38).