The ratio of two numbers is 8 to 5. The difference of the numbersis 24. What are the numbers?

Question

what is the answer to this problem? Don't know how to work it out.

Answer 1

Hi Melynn,

 

If the ratio of two numbers is 8 to 5, that means that they could be 8 and 5 or 16 and 10 (if you multiply 8 times 2 and 5 times 2, you get 16 and 10), or 24 and 15 (by multiplying by 3) or . . . .

 

It can be written as 8/5 which means 8 divided by 5.  24/15 reduces to 8/5 by dividing top and bottom by 3

 

Since we don't know what the numbers are, we'll call them X and Y.

 

So X/Y = 8/5

 

When there are two variables, you need two equations to solve.

 

Luckily they give you another one!

 

The difference of the number is 24.  Difference means subtraction.

 

So X - Y = 24

 

You could also write Y - X = 24 but we'll stay with  X - Y.

 

If you add Y to both sides of the equation you get X = 24 + Y

 

Now we can substitute this value of X into the first equation--> (24 + Y)/Y = 8/5

 

Now cross multiply (top of one fraction times bottom of the other)--> 5(24 + Y) = 8Y

 

Multiply 5 times what's in the parentheses--> 120 + 5Y = 8Y

 

Subtract 5Y from both sides--> 120 = 3Y

 

Divide both sides by 3--> 40 = Y

 

Then X must be 64 if their difference is 24.

 

Check and see if their ratio reduces to 8/5. . . this will confirm the answer.

 

Have fun.

 

Dan

Answer 2

X/Y = 8/5

 

X - Y = 24

 

X = 24 + Y

 

(24 + Y)/Y = 8/5

 

24/Y + 1 = 8/5

 

3Y = 120

 

Y = 40

 

X = 64