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Ann is 3 years old and Laura is 6 years old. Explanation: Let L be Laura's age and A be Ann's age.

Product means multiply, so LA is the product of their ages

The sum of their ages is L+A

So we have LA=2(L+A)

This simplifies to LA=2L+2A

Now we also know L is 3 years older than A so L=3+A

So we have (3+A)A=2(3+A)+2A 3A+A^2=6+2A+2A or 3A-4A+A^2-6=0 or A^2-A-6=0

Now we can factor (A-3)(A+2)=0 so A is 3 or -2 3 makes sense, -2 as an age does not.

So Ann is 3

Laura is 3 years older so she is 6.

Now let's check 3x6=18 And 3+6=9 and 9x2 =18 as desired so it works!

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Q: Anna 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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