1. Let S represent the cost of the sofa and C represent the cost of the chair.
If the sofa costs $50 less than three times the cost of the chair, then effectively we can write this as:
S = 3C - 50
If the sofa and chair together cost $650, we can write this as:
S + C = 650
2. Now, we can find out how much the sofa and chair cost by solving the two equations we obtained above for C, and substituting S = 3C - 50 into S + C = 650. Thus, we get:
S + C = 650
if S = 3C - 50, then:
3C - 50 + C = 650
4C - 50 = 650 (Add C and 3C)
4C = 700 (Add 50 to both sides)
C = 175 (Divide both sides by 4)
Thus, the cost of the chair is $175. Now, to find the cost of the sofa we need to simply substitute C = 175 into our first equation, S = 3C - 50:
S = 3(175) - 50
S = 525 - 50
S = 475
Thus, the sofa costs $475.
3. Now that we know that the sofa costs $475 and the chair costs $175, all we need to do is to subtract the cost of the chair from the cost of the sofa to find the difference in price:
475 - 175 = 300
Therefor, the sofa costs $300 more than the chair (answer C).