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?
+177 Amy is attempting to redecorate the apartment. From the problem statement, Amy has purchased the following items:
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!
