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18 July, 07:58

A sofa 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

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Answers (2)
  1. 18 July, 10:19
    0
    C. 300 is the answer
  2. 18 July, 11:35
    0
    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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