The sum of two numbers is 10 and the sum of their reciprocals is 5/12. Find the numbers. Please help, I figured the answer out but I still don\'t get how I got it. I want the whole problem solved. Solution Let A , and B represent the numbers. A  +   B   = 10 1/A  + 1/B  = 5/12 Find the common denominator for A, B   which is AB       by multiplying B by 1 and A, and multiplying A by 1 and B The second equation will be (A+B)/AB = 5/12 we know that A+B = 10 You now have  10/AB = 5/12 cross multiply and solve for AB 10x12=5AB 120 = 5AB   divide both sides by 5 24 = AB We now have A + B = 10 AB  = 24 Divide both sides by B A = 24/B Substitute A in Equation 1 24/B + B =10 Multiply each term by B 24 + B^2 = 10B Subtract 10B from both sides B^2 -10B +24 = 0 (B-6)(B-4) = 0 B= 6, and B=4 If B = 6, then A =4 Your two numbers are 6 and 4. (B + A)/AB = 5/12 .

1. The sum of two numbers is 10 and the sum of their reciprocals is 5/12. Find the numbers.
Please help, I figured the answer out but I still don't get how I got it. I want the whole problem
solved.
Solution
Let A , and B represent the numbers.
A + B = 10
1/A + 1/B = 5/12
Find the common denominator for
A, B which is AB by multiplying B by 1 and A, and multiplying A by 1 and B
The second equation will be
(A+B)/AB = 5/12
we know that A+B = 10
You now have 10/AB = 5/12
cross multiply and solve for AB
10x12=5AB
120 = 5AB divide both sides by 5
24 = AB
We now have A + B = 10
AB = 24
Divide both sides by B
A = 24/B

2. Substitute A in Equation 1
24/B + B =10
Multiply each term by B
24 + B^2 = 10B
Subtract 10B from both sides
B^2 -10B +24 = 0
(B-6)(B-4) = 0
B= 6, and B=4
If B = 6, then A =4
Your two numbers are 6 and 4.
(B + A)/AB = 5/12