Asofa costs $50 less than three times the cost of a chair. if the sofa and chair together cost $650, how much more does the sofa cost than the chair? a) $175 b) $225 c) $300 d) $475

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).

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