1. Take into account that the relation between yards of fabric and elf costumes is linear. The the general form of the equation is of such a relation is:
y = kx
where k is the constant of proportionality.
In order to calculate k, calculate the quotient between the number of yards Mrs. Henderson used and the number of elf costumes He made with such a quantiy of yards of fabric:
k = (6 3/4)/3
conver 6 3/4 to a normal fraction:
6 3/4 = 6 + 3/4 = (24 + 3)/4 = 27/4
Then, you obtain for k:
k = (27/4)/(3) = 27/12
Hence, the equation that relates number of yards of fabric with the number of elf costumes made is:
y = (27/12)x
2. For 7 elf costumes you have:
y = (27/12)(7) = 15.75
Hence, it is necessary to use 15.75 yards of fabric to make 7 elf costumes