Find two numbers such that their product, sum and difference are in the ratio 5:4:1'

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.