The sum of the age of two brothers is 22 years. Six years ago, the product of their ages was 21. Find the age of the elder brother.

The elder brother is 13 years old

Step-by-step explanation:

System of equations

Let's set:

x=current age of the younger brother

y=current age of the elder brother

The first condition states the sum of their ages is 22:

x + y = 22

It follows that:

x = 22 - y

Their ages six years ago were: x-6 and y-6. The product of both is 21:

( x - 6 ) ( y - 6 ) = 21

Replacing the expression of x:

( 22 - y - 6 ) ( y - 6 ) = 21

Simplifying:

(16 - y ) ( y - 6 ) = 21

Multiplying:

Rearranging and simplifying:

Applying the quadratic solver:

Where a=1, b=-22, c=117

There are two possible solutions:

The value of x could have two solutions also:

x=22-13=9

x=22-9=13

Since y is the age of the elder brother, the answer is:

The elder brother is 13 years old

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