# The difference between two numbers is 12. Three times the larger number is seven times the smaller. What are the two numbers?

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Let us say the two numbers are x and y and x>y.

The data we have are;

- Difference between the numbers are 12.
- 3 times larger number is equal to 7 times smaller number.

Then we can write;

`x-y = 12 ` ----(1)

`3x = 7y ` ----(2)

From (1) we can say `x = (12+y)`

Then substituting `x = (12+y)` to (2) gives;

`3(12+y) = 7y`

`36+3y = 7y`

`4y = 36`

`y = 9`

Then;

`x = 12+y`

`x = 12+9 = 21`

*So the two numbers are 21 and 9.*

Let x be the larger number and y the smaller number.

(1) The difference between the numbers is 12 so x-y=12

(2) Three times the larger equals seven times the smaller means 3x=7y

From (1) we have x=12+y.

Substituting into (2) we get 3(12+y)=7y

36+3y=7y

36=4y

y=9 so x=21

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**The numbers are 21 and 9**

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Check: 3(21)=7(9)=63 and 21-9=12 as required.