Question

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.

Answer 1

(CREDIT TO ANSWER BEFORE ME FOR 5 5/7, 50 3/14)

The numbers are 5 5/7, 50 3/14 or 9 5/42, 53 13/21

Explanation:

LOOK UP FOR EXPLANATION FOR THIS ANSWER SET: 5 5/7, 50 3/14

BUT JUST IN CASE I'LL PASTE THE WORK HERE

(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

SECOND ANSWER SET: 9 5/42, 53 13/21

From the equation, we know that x-y=44 1/2 and 7y-x=10 3/14.

Using x-y=44 1/2 we can figure out that x=44 1/2+y. We can substitute x=44 1/2+y into 7y-x=10 3/14, the equation would then become 7y-44 1/2-y=10 3/14. Then we solve that equation and we can get y=9 5/42.

Going back to x=44 1/2+y, we can find x by adding 44 1/2 to 9 5/42, which would get us 53 13/21

Answer 2

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