## Age Ratio

The solution is as follows:

We will call **y** the age of the youngest person.

We will call **x** the age of the oldest person.

The problem is that now (currently) the ages are in the 4 to 5 ratio. So:

y / x = 4/5 (equation 1)

The problem is that 8 years ago the ages were in the ratio of 8 to 11. So:

(y-8) / (x-8) = 8/11 (equation 2)

Isolating y in equation 1:

y = 4x / 5

Putting this value of y in equation 2 we have:

((4x / 5) -8) / (x-8) = 8/11

(4x / 5) -8 = 8/11. (X-8)

Making the mmc on both sides we have:

(4x-40) / 5 = (8x-64) / 11

11. (4x-40) = 5. (8x-64)

44x-440 = 40x-320

44x-40x = 440-320

4x = 120

x = 30

**So the age of the oldest person is 30 years old !!!**

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