Answer:
the two numbers are 8 and 6
Step-by-step explanation:
we can write multiple equations based off this
1. 7(x-y) = x+y
simplifying our first equation
7x-7y = x + y
6x = 8y
x = 4y/3
2. 24(x-y) = xy
plugging in our known value for y
24(y/3) = [tex]\frac{4y^2}{3}[/tex]
8y = 4y^2/3
multiplying both sides by 3
24y = [tex]4y^2[/tex]
dividing both sides by 4,
do not divide both sides by y, this will remove a possible solution
6y = y^2
y^2-6y = 0
y(y-6) = 0
y = 0, 6
finding the x values for the corresponding y
if y= 0, x = 0
if y = 6, x = 8
testing (0,0) (writing the 2 numbers as a point to make it easier)
0-0 = 0
0+0 = 0
0*0 = 0
0 : 0 : 0 is not the same ratio as 1:7:24
testing (8,6)
8-6 = 2
8+6 = 14
8*6 = 48
2:14:48 = 1:7:24 (divide the first ratio by 2)
