Find abc

[greatwhiteshark]

If a, b, and c are positive real numbers such that a(b+c) = 152, b(c+a) =
162 and c(a+b)= 170, then abc is...?

a)672 b)688 c)704 d)720 e)750

 

[wjm11]

If a, b, and c are positive real numbers such that a(b+c) = 152, b(c+a) =
162 and c(a+b)= 170, then abc is...?

a)672 b)688 c)704 d)720 e)750

What have you tried?

Did you mean "a, b, and c are positive integers"? If that assumption is made, and you factor the numbers 152, 162, and 170, you can arrive at a series of possible values for each of a, b, and c.

You can also distribute and combine eqns. For example, subtract eqn1 from eqn2 and add eqn3 to find that bc = 90. Hmmm, what two possible values of b and c (that we found by factoring) multiply to yield 90? Get the idea?

a = 8, b = 9, and c = 10 is a (non-rigorous) solution.

 

[greatwhiteshark]

My Reply

8 x 9 x 10 = 720. Is this the answer?