The difference of two numbers is 44 1 /2 . if the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . find the numbers. the numbers are or i've spent 4 hours on this problem.

Let’s call the numbers x and y. Let’s also say that x is the smaller of the two. Since their difference (the answer you get when you subtract is 44 and a half) we know that y-x=44.5

Next we are told that if the smaller increases 7 times (that means 7x) their difference would be 10 3/14. Let’s write that as a fraction. It is 14x10+3 over 14. That is 143/14.

So this means y-7x=143/14.

We have two equations and two unknowns (a system of equations). We write one over the other and subtract them to get:

y-x=44.5
y-7x=143/14

Subtracting yields:
(y-y)+(-x - - 7x) = 44.5 - 143/14
6x = (89/2) - (143/14)
6x= 623/14 - 143/14
6x=480/14
X= (480/14)(1/6)
X=80/14
x= 40/7 = 5 5/7

Since y-x=89/2
We get y - 40/7 = 89/2
Y = 40/7 + 89/2
Y = 80/14 + 623/14
Y = 703/14 = 50 3/14