Answer:
The sum of the two numbers is 12.5
Step-by-step explanation:
First we write a system of equations.
One number is 4 times larger than the other.
y = 4x
The sum of their reciprocals is 1/2
1/x + 1/y = 1/2
Substitute
1/x + 1/4x = 1/2
1 + 1/4 = 1/2x
x = 2.5
Solve for other number
y = 4(2.5)
y = 10
The inverse of x is 2/5 or 4/10, and the inverse of y is 1/10. When added the sum is 5/10 or 1/2.
