Find two numbers that have a difference of 24 and a quotient of 5.

Question

Find two numbers that have a difference of 24 and a quotient of 5.

Thanks

Answer 1

n represents one number

n + 24 represents the other number

 

(n + 24) / n = 5

n + 24 = 5n

24 = 4n

6 = n

 

The two numbers are 6 and 30.

Answer 2

You are looking for two unknown numbers, so you need to set up a system of 2 equations to solve this problem. First:

 

x-y=24

 

then

 

x/y=5

 

Next, solve the first equation for x:

 

x=y+24

 

Then substitute that into your second equation:

 

(y+24)/y=5

 

There are many ways to go from here, the easiest might be this:

 

(y/y) + (24/y) = 5........and of course (y/y)=1, so:

 

1+(24/y)=5

 

(24/y)=4

 

Then multiply both sides by y:

 

24=4y

 

Then divide both sides by 4:

 

y=24/4=6

 

Now you know y=6, so plug that into the first equation:

 

x-6=24

 

x=30

 

So there are your two numbers: 30 and 6

 

30-6=24 and 30/6=5   Viola!

 

 

Let me know if you need any more help!