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Charlie is older than Ava. Their ages are consecutive even integers. Find Charlie's age if the product of their ages is 80

User Gurjeet
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1 Answer

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Let's start by assigning variables to the ages of Charlie and Ava.

Let x be the age of Ava, then Charlie's age is x + 2 (since their ages are consecutive even integers).

We know that the product of their ages is 80, so we can set up the equation:

x(x + 2) = 80

Expanding the left side:

x^2 + 2x = 80

Subtracting 80 from both sides:

x^2 + 2x - 80 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = 2, and c = -80:

x = (-2 ± sqrt(2^2 - 4(1)(-80))) / 2(1)

Simplifying:

x = (-2 ± sqrt(324)) / 2

x = (-2 ± 18) / 2

x = -10 or x = 8

Since we are looking for a positive age, Ava is 8 years old, and Charlie is x + 2 = 10 years old.

Therefore, Charlie is 10 years old.
User Nick Rempel
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