SOLUTION: If a,b, and c are positive integers, find the sum a + b + c if: {{{a^3b^3c = 454425283}}}, {{{a^3bc^3 = 248258803}}} and {{{ab^3c^3 = 777094123}}}

Algebra ->  Exponents -> SOLUTION: If a,b, and c are positive integers, find the sum a + b + c if: {{{a^3b^3c = 454425283}}}, {{{a^3bc^3 = 248258803}}} and {{{ab^3c^3 = 777094123}}}      Log On


   

Question 1199209: If a,b, and c are positive integers, find the sum a + b + c if:
a%5E3b%5E3c+=+454425283, a%5E3bc%5E3+=+248258803 and ab%5E3c%5E3+=+777094123
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


For this one, you definitely want to use an online calculator to find the prime factorization... unless you have nothing better to do with your time.

454425283 = (13^3)(17^1)(23^3)

You could use the online calculator again to find the prime factorizations of the other two numbers. But you don't have to, because you already know that

(a^3)(b^3)(c) = (13^3)(17)(23^3),

so you know that c is 17 and a and b are, in some order, 13 and 23. And since you are only asked to find the sum a+b+c, you have all the information you need to do that.

ANSWER: a+b+c = 13+17+23 = 53