SOLUTION: A, B and C are whole and positive numbers. A+B+C=38 and A*B*C=630. What are the numbers? How do I find that out with three variables and only two equations? Thanks so much!

SOLUTION: A, B and C are whole and positive numbers. A+B+C=38 and ABC=630. What are the numbers? How do I find that out with three variables and only two equations? Thanks so much!

Question 274951: A, B and C are whole and positive numbers.
A+B+C=38 and A*B*C=630. What are the numbers?
How do I find that out with three variables and only two equations?
Thanks so much!
Gu�r�n
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Because we're only looking for positive integer solutions, this set of solutions will be finite even though we're missing a third equation. To find these solutions, simply list all of the factors of 630 and see which set of 3 factors add up to 38. For example, 630=2*5*63 which means that 2+5+63=70.

It turns out that there are only 6 sets of solutions and they are

A = 2, B = 15, C = 21
A = 2, B = 21, C = 15
A = 15, B = 2, C = 21
A = 15, B = 21, C = 2
A = 21, B = 2, C = 15
A = 21, B = 15, C = 2

For example, when A = 2, B = 15, C = 21, then 2*15*21=630 and 2+15+21=38

Basically, there are 3 unique numbers here (they're just being rearranged) and the numbers are 2, 15, and 21.
RELATED QUESTIONS
1.) I. a, b and c are whole numbers,... (answered by richwmiller)

given that A,B,C and D are whole numbers such that A*B=8, B*C=28, C*D=63 and B*D=36, find (answered by tommyt3rd)

given that A,B,C and D are whole numbers such that A+B=8, B+C=11,B+D=13 and C+D=14, find... (answered by Cromlix,tommyt3rd)

given that A,B,C and D are whole numbers such that A*B=8,B*C=28,C*D=63 and B*D=36, find... (answered by tommyt3rd)

given that A,B,C and D are whole numbers such that A+B=8, B+C=11, B+D=13 and C+D=14, find (answered by tommyt3rd)

If a, b, and c are positive numbers such that √a/√b = 8c and ac = b what is... (answered by ankor@dixie-net.com)

suppose that a,b,c and d are positive numbers such that a/b < c/d show that a/b <... (answered by richard1234)

a, b, and c are three positive numbers. If a is 3/5 of c and b is 1/2 of c, then a is... (answered by mananth)

if a,b,c are positive real numbers such that a(b+c)=152 b(c+a)=162 and c(a+b)=110 then... (answered by Alan3354)