Answer:
3 1/3 and 2
Step-by-step explanation:
Let the numbers be x and y and let z be the constant of proportion. Then
xy = 5z ...............(1)
x + y = 4z ...........(2)
x - y = z ..............(3) Adding (2) and (3)
2x = 5z
x = 5z/2 ................(4)
Substituting for x in equation 1:
5z/2 * y = 5z
y = (5z * 2) / 5z = 2.
Substituting for y in equations (2) and (3):
x + 2 = 4z
x - 2 = z Subtracting:
4 = 3z
z = 4/3.
Substituting for z in equation (4)
x = 5(4/3) /2
x = 20/6 = 10/3 = 3 1/3.
So the 2 numbers are 3 1/3 and 2.
Checking the results:
xy = 2 * 10/3 = 20/3 = 5 * 4/3 = 5z
x + y = 10/3 + 2 = 16/3 = 4 * 4/3 = 4z.
x - y = 10/3 - 2 = 4/3 = z.