SOLUTION: If A+B=45 & 1/A + 1/B=1/10 then find A & B

Question 712166: If A+B=45 & 1/A + 1/B=1/10 then find A & B
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
If A+B=45 & 1/A + 1/B=1/10 then find A & B
.
Solve for B:
A+B=45
B=45-A
Substitute above into:
1/A + 1/B=1/10
1/A + 1/(45-A) = 1/10
multiply both sides by LCD of 10A(45-A):
10(45-A) + 10A = A(45-A)
450-10A + 10A = 45A-A^2
450 = 45A-A^2
A^2+450 = 45A
A^2-45A+450 = 0
(A-30)(A-15) = 0
A = {15, 30}
.
Since B=45-A
B = {30, 15}
.
Solution:
(A,B) = (15, 30)
OR
(A,B) = (30, 15)

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