Question

To sew holiday tablecloths for the school dance, Mrs. Stitcher bought four more than three times as many yards of red fabric than of gold fabric. If she bought a total of 112 yards, how many yards of each color did she buy?

Answers

  2. Answer:

    Mrs. Stitcher bought 27 yards of red fabric and 85 yards of gold fabric, respectively.

    Step-by-step explanation:

    Let be x and y the total of red and gold fabric, measured in yards. After a careful reading of statement, we get the following two linear equations:

    Red fabric vs. Gold fabric

    3\cdot x +4 = y (Eq. 1)

    Total fabric amount

    x+y = 112\,yd (Eq. 2)

    Then, we reduce the current system of equation into a sole equation by elimination: (Eq. 1) in (Eq. 2)

    x+(3\cdot x +4) = 112

    4\cdot x +4 = 112

    4\cdot x = 108

    x = \frac{108}{4}

    x = 27

    Then,

    y = 112 - x

    y = 112 - 27

    y = 85

    Mrs. Stitcher bought 27 yards of red fabric and 85 yards of gold fabric, respectively.

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