Amy is redecorating her apartment. She went to the local craft store and purchased 3and 1 over 2 yards of zebra print fabric, 4 feet of hot pink ribbon, and 2and 1 over 4 yards of lime green material. How many feet and inches of fabric did Amy purchase?

 Sep 1, 2023

Amy is attempting to redecorate the apartment. From the problem statement, Amy has purchased the following items:

  1. \(3\frac{1}{2}\) yards of zebra print
  2. 4 feet of hot pink ribbon
  3. \(2\frac{1}{4}\) yards of line green material

Our objective is to determine the total amount of fabric in feet and inches. Since some of the units is given in yards, we need to perform a conversion so that we can compare common units. Since one of the units is already given as feet, I will convert all units to feet out of convenience. It turns out that \(1 \text{ yard} = 3 \text{ feet}\). We can use this equivalence to convert the given units into yards.


\(3\frac{1}{2} \text{ yards} * \frac{3 \text{ feet}}{1 \text{ yards}} = \frac{7}{2} \text{ yards} * \frac{3 \text{ feet}}{1 \text{ yards}} = \frac{21}{2} \text{ feet}\)

\(2\frac{1}{4} \text{ yards} * \frac{3 \text{ feet}}{1 \text{ yards}} = \frac{9}{4} \text{ yards} * \frac{3 \text{ feet}}{1 \text{ yards}} = \frac{27}{4} \text{ feet}\)


Now that all the units are common, we can perform addition. We use the common denominator to add these fractions together.


\(\begin{align*} \frac{21}{2} \text{ feet} + 4 \text{ feet} + \frac{27}{4} \text{ feet} &= \frac{42}{4} \text{ feet} + \frac{16}{4} \text{ feet} + \frac{27}{4} \text{ feet} \\ &= \frac{42 + 16 + 27}{4} \text{ feet} \\ &= \frac{85}{4} \text{ feet} \\ &= 21\frac{1}{4} \text{ feet} \end{align*} \)


The question states that the answer should be given in the units of feet and inches. While this technically satisfies the condition, I am guessing that you would like a whole number of feet and whole number of inches as the final answer. We can convert the final \(\frac{1}{4} \text{ feet}\) to inches to meet this condition. The conversion factor between feet and inches is \(1 \text{ foot} = 12 \text{ inches}\).


\(\frac{1}{4} \text{ feet} * \frac{12 \text{ inches}}{1 \text{ feet}} = 3 \text{ inches}\)


Now that we have converted the fractional part to a whole number of inches, we can write the final answer as \(21 \text{ feet}\; 3 \text{ inches}\) of total fabric!

 Sep 3, 2023

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