Huzefa K. answered • 11/13/14

Math Teacher|Michigan + Northwestern Law|Perfect Score Math ACT + SAT

**L is 3 years old.**To find A's age, we just plug L's age back into either equation. We will use the first one since it's simpler:

**A is 6 years old.**

Tina S.

asked • 11/13/14Anna is 3 years older than Laura. The product of their ages is double the sum of their ages. How old are they?

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Huzefa K. answered • 11/13/14

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Math Teacher|Michigan + Northwestern Law|Perfect Score Math ACT + SAT

Hi Tina-

Here is how you solve this one. You need two equations, one representing each of the relationships mentioned above. First, we will use the following variables to represent each person:

Anna = A

Laura = L

Next, here are the equations:

A = L + 3

A*L = 2(A + L)

Now, solving an equation with two variables is not doable. So, we use substitution to get one of the equations down to a single variable. we substitute a value for A into the second equation to have only L.

(L + 3)*L = 2((L + 3) + L)

L^2 + 3L = 4L + 6

L^2 - L - 6 = 0

Now we have a quadratic equation that we must solve by factoring. So, we get:

(L - 3)(L + 2) = 0

L = 3 or -2

We can eliminate the second answer as it is negative, so **L is 3 years old.** To find A's age, we just plug L's age back into either equation. We will use the first one since it's simpler:

A = L + 3

A = 3 + 3

A = 6

Nicole H. answered • 11/13/14

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Knowledgeable and Motivated Chemistry and Algebra tutor

Tina,

If Anna's age is A and Laura's age is L

Anna is 3 years older than Laura, therefore A = L + 3

Product of their ages = 2 (sum of their ages), therefore A x L = 2 (A + L)

Let's substitute L + 3 for A in the second equation: (L+3) x L = 2 (L+3 + L)

L^{2} + 3L = 2L + 6 + 2L

L^{2} + 3L = 4L + 6

L^{2} - L - 6 = 0

Factor this quadratic equation: (L - 3) (L + 2) = 0

L = 3 or L = -2

L = -2 is not possible since your age cannot be negative.

Therefore, Laura's age is 3 and Anna's age is 6

Check solution: 3 x 6 = 2 (3 + 6)

18 = 18

Hope it helps

Keith M. answered • 11/13/14

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Keith - Tutoring mathematics from middle up to college mathematics

Laura is 2 and Anna is 5.

x^{2} = 2x

x = 2

Substitute x = 2 into...

x + 3 = Anna's Age

x = 2 = Laura's Age

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