Two numbers are such that their difference, their sum and their product are in the ratio 1:7:24. Find the numbers.

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) =

8y = 4y^2/3

multiplying both sides by 3

24y =

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)

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step-by-step explanation: