Answer:
Step-by-step explanation:
Let's start simple here. If I was in my Algebra class, I'd tell my students to "baby step" this. Basically, what we are looking for is how much red fabric plus how much gold fabric equals 112, the total amount of fabric she bought. That, as an equation, is r + g = 112. But since we have only one equation we are working with, we can only have one unknown. So we need to write red fabric in terms of gold, or gold fabric in terms of red. We are told in the problem that the amount of red fabric is "four more than three times as many yards as gold". As an expression, that is r = 3g + 4. Now what we are going to do is sub in 3g+4 for r in the original equation.
3g + 4 + g = 112 and
4g + 4 = 112 and
4g = 108 so
g = 27. She bought 27 yards of gold and 112 - 27 yards of red, which is 85 yards
She bought 27 yards of gold fabric and 85 yards of red fabric
Let the number of gold fabrics be represented by g
Therefore, the number of red fabric will be = 3g + 4
Therefore, the equation to solve the question will be:
3g + 4 + g = 112
Collect like terms
4g + 4 = 112
4g = 112 - 4
4g = 108
Divide both side by 4
4g/4 = 108/4
g = 27
She bought 27 yards of gold fabric.
The yards of red fabric will be:
= 3g + 4
= 3(27) + 4
= 81 + 4
= 85 yards
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