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

Answer:

3, 7

Step-by-step 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:

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