Question

One number is 2 more than 3 times another. Their sum is 22. Find the numbers.

Answer 1

Make a system of equations.

$\sf~x=3y+2$
$\sf~x+y=22$

Re-arrange the 2nd equation:

$\sf~x+y=22$

Subtract y to both sides:

$\sf~x=-y+22$

Plug in -y + 22 for 'x' in the first equation.

$\sf~x=3y+2$

$\sf~-y+22=3y+2$

Subtract 3y to both sides:

$\sf~-4y+22=2$

Subtract 22 to both sides:

$\sf~-4y=-20$

Divide -4 to both sides:

$\sf~y=\boxed{\sf5}$

Plug this into any of the two equations to find 'x':

$\sf~x+y=22$

$\sf~x+5=22$

Subtract 5 to both sides:

$\sf~x=\boxed{\sf17}$

So one of the numbers is 5 and one of them is 17.