Question

The ratio of the sum of two numbers to the difference of the two numbers is 9. The product of the two numbers is 80. Find the numbers.

Answer 1

There are two equations here:

(a+b)/(a-b) = 9 and ab=80

the first one simplifies to 8a = 10b or a = (4/5)b.

You can plug this last part in for 'a' in the second equation:

(4/5)b*b = (4/5)b^2 = 80 which means b^2 = 64 or b = +8 or -8.

I guess the question asks for the positive solution, so then you will find that a = 10 if you plug the value of b in for one of the original equations. Then your final answer would be a = 10 and b = 8. But, there is another solution, I believe, that is a = -10 and b = -8, since ab would still equal 80 and (a+b)/(a-b) would be -18/-2 which still equals 9. Notice that either a and b are both positive or both negative, because this is the only time that the product of both numbers would be also positive.