Problem:
The difference of two numbers is 7. Their product is 144. Find the numbers.
Solution:
let x and y be the numbers
x - y = 7 equation 1
x = 7 + y equation 1
xy = 144 equation 2
if x = 7 + y
xy = 144
(7 + y)(y) = 144
7y + y² = 144
y² + 7 y - 144 = 0
(y - 9) (y + 16) = 0
y = 9 ; y = - 16
use the positive value of y = 9 to substitute for equation 1
x = 7 + y
x = 7 + 9
x = 16
xy = 144
y = 144 / x
y = 144/16
y = 9
Checking:
x - y = 7
16 - 9 = 7
7 = 7 ; ok
xy = 144
16(9) = 144
144 = 144 ; ok
Answer:
x = 16
y = 9
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