SOLUTION: The difference between two numbers is 12 and twice the larger is three times the smaller. What is the smaller number?

Click here to see ALL problems on Unit Conversion Word Problems

Question 918079: The difference between two numbers is 12 and twice the larger is three times the smaller. What is the smaller number?
Found 2 solutions by CubeyThePenguin, greenestamps:
Answer by CubeyThePenguin(3113) (Show Source):
You can put this solution on YOUR website!
x = larger number
y = smaller number

x - y = 12
2x = 3y

Plug in x = 3y/2 into equation 1.

3y/2 - y = 12
y/2 = 12
y = 24

The numbers are 36 and 24.

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

Since twice the larger is equal to three times the smaller, the two numbers are in the ratio 3:2.

So the two numbers can be represented by 3x and 2x.

The difference between 3x and 2x is 3x-2x=x.

But the difference between the numbers is 12, so x=12.

And then the two numbers are 3x=36 and 2x=24.

ANSWER: The smaller number is 24.