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The product of the ages of Cally and Katy is 130 less than the product of their ages in 5 years. If Cally is 3 years older than Katy, what are their current ages?

Question

The product of the ages of Cally and Katy is 130 less than the product of their ages in 5 years. If Cally is 3 years older than Katy, what are their current ages?

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Solution

Let's denote Katy's current age as x. Then, Cally's current age would be x + 3 (since Cally is 3 years older than Katy).

According to the problem, the product of their ages in 5 years (which would be (x+5) for Katy and (x+3+5) for Cally) is 130 more than the product of their current ages. This gives us the equation:

(x)(x+3) + 130 = (x+5)(x+8)

Solving this equation will give us their current ages.

First, simplify the equation:

x^2 + 3x + 130 = x^2 + 13x + 40

Subtract x^2, 3x from both sides:

130 = 10x + 40

Subtract 40 from both sides:

90 = 10x

Finally, divide by 10:

x = 9

So, Katy is 9 years old and Cally, being 3 years older, is 12 years old.

This problem has been solved

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