Question

Three times a larger number added to 4 times a smaller number totals 24. When twice the smaller number is subtracted from twice the larger number, the result is 2. What are the two numbers?

Answer 1

Answer: The two numbers are 3 and 4.

Explanation:

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

Three times a larger number added to 4 times a smaller number totals 24.

`3x+4y=24------------------(1)\\\\2x-2y=2\\\Rightarrow\ x-y=1\\\Rightarrow\ x=1+y-----------------(2)`

`3(1+y)+4y=24\\\\\Rightarrow\ 3+3y+4y=24\\\\\Rightarrow\ 7y=21\\\\\Rightarrow\ y=3`

Substitute y=3, in equation (2), we get

`x=1+3=4`

Hence, the two numbers are 3 and 4.