Question

One number added to three times another is 24. Five times the first number added to three times the other number is 36. Find the numbers.

Answer 1

3, 7

Explanation:

Substitute "one number", etc., with variables:

`a+3b=24\\5a+3b=36`

This gives us a solvable system of equations. To solve this, solve for a in the first equation:

`a+3b=24\\a=24-3b`

Substitute a into the second equation and simplify:

`5a+3b=36\\5(24-3b)+3b=36\\120-15b+3b=36\\120-12b=36\\-12b=-84\\b=7`

Substitute the value of b into the first equation:

`a+3(7)=24\\a+21=24\\a=3`