The sum of two numbers is 334 one number is 18 less than seven times the other find the numbers

Let's make 2 equations.

A+B=334

A = 7B-18

Let's replace a in the first equation with the second equation.

7B-18+B=334

Simplify.

8B-18=334

add 18 to both sides.

8B = 352

Divide.

352:8

44

So, one number is 44. Let's put 44 for B in the first equation in order to find a.

A+44=334

334-44

290

So a equals 290. Let's make sure by using the second equation.

7 (44) - 18

308-18

290

One number equals 44, while another number equals 290.