Answer:
Mrs. Stitcher bought 27 yards of red fabric and 85 yards of gold fabric, respectively.
Step-by-step explanation:
Let be [tex]x[/tex] and [tex]y[/tex] 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
[tex]3\cdot x +4 = y[/tex] (Eq. 1)
Total fabric amount
[tex]x+y = 112\,yd[/tex] (Eq. 2)
Then, we reduce the current system of equation into a sole equation by elimination: (Eq. 1) in (Eq. 2)
[tex]x+(3\cdot x +4) = 112[/tex]
[tex]4\cdot x +4 = 112[/tex]
[tex]4\cdot x = 108[/tex]
[tex]x = \frac{108}{4}[/tex]
[tex]x = 27[/tex]
Then,
[tex]y = 112 - x[/tex]
[tex]y = 112 - 27[/tex]
[tex]y = 85[/tex]
Mrs. Stitcher bought 27 yards of red fabric and 85 yards of gold fabric, respectively.
