An equation is formed of two equal expressions. The amount of fabric that will be needed for making 7 costumes is 15 3/4 yards.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that Mr. Henderson used 6 3/4 yards of fabric to make 3 elf costumes. Therefore, we can write the relation between the amount of fabric needed and the Number of costumes as,
Amount of fabric needed ∝ Number of costumes
If the total number of yards of fabric is represented by y and the total number of costumes is represented by x, then we can write,
y ∝ x
y = kx
6 3/4 yards = k × 3 costumes
(6×4 + 3)/4 yards = k × 3 costumes
27/4 yards = k × 3 costumes
k = 27/(4×3) yards per costume
k = 9/4 yards per costume
Thus, the equation can be written as y = (9/4)x.
Further, the amount of fabric that will be needed is,
Amount of fabric for 7 costumes, y = (9/4)x
= (9/4) × 7
= 63/4
= 15 3/4 yards
Hence, the amount of fabric that will be needed for making 7 costumes is 15 3/4 yards.
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