Raul and ruth are saving for a trip. raul starts with $350 and saves $15 per week. ruth starts with $200 and saves $25 per week. when will they have the same amount?

Develop two linear equations to represent the savings of these two people:
Raul:  rl=$350 + $15x
Ruth:  rh=$200 + $25x
In both cases, x represents the number of weeks elapsed.

When will these two people have saved up the same amount?  Set rl = rh and solve for x, the number of weeks elapsed:

$350 + $15x = $200 + $25x

$150 = $10x           gives us x= 15.  Their savings will be equal after 15 weeks.