SOLUTION: George is 2 more than twice the age of alice. The product of their ages is 84. What are their ages?

Question 535775: George is 2 more than twice the age of alice. The product of their ages is 84. What are their ages?
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
Let G = George's age now
Let A = Alice's age now
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Given:
G = 2A + 2
G * A = 84
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With two equations and two unknowns, restate one of the equations in terms of the other variable (unknown) and substitute that equality back into the other equation. In this case, we already have G in terms of A, so let's plug that one into the 2nd equation:
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(2A + 2) * A = 84
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Simplify:
2A^2 + 2A = 84
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Subtract 84 from both sides and now we have a quadratic equation in standard form:
2A^2 + 2A - 84 = 0
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We can divide both sides by 2 to simplify further:
A^2 + A - 42 = 0
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Then factor the quadratic equation to solve for the roots:
(A + 7)(A - 6) = 0
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This says that A = -7, or 6 are possible solutions; however, Alice = -7 years old doesn't make any sense, so you can reject that possible solution.
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A = 6 lets us go back to either of the original equations to solve for G. We already have an equation for G in terms of A, so use that one:
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G = 2A + 2
G = 2(6) + 2
G = 14
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A = 6, G = 14
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Check your work:
G * A = 84
14 * 6 = 84
84 = 84 checks
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George is 14 yrs old
Alice is 6 yrs old
Problem solved
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Cheers,
Lee
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