Question

mary is making some shirts for her schools drama department. the fabric store has $3\frac{1}{6}$ yards of the fabric she wants in stock. but this quantity of fabric can make only $1\frac{1}{3}$ shirts. what length of fabric does mary need to buy if she wants to sew 2 shirts?\
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a. $4\frac{3}{4}$ yards\
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b. $3\frac{5}{6}$ yards\
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c. $1\frac{1}{6}$ yards\
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d. $2\frac{3}{8}$ yards

Explanation:

Step1: Find fabric per shirt

First, convert mixed numbers to improper fractions. \(3\frac{1}{6}=\frac{19}{6}\) and \(1\frac{1}{3}=\frac{4}{3}\). To find fabric per shirt, divide total fabric by number of shirts: \(\frac{19}{6}\div\frac{4}{3}=\frac{19}{6}\times\frac{3}{4}=\frac{19}{8}\) yards per shirt.

Step2: Calculate fabric for 2 shirts

Multiply fabric per shirt by 2: \(\frac{19}{8}\times2=\frac{19}{4}=4\frac{3}{4}\) yards. Wait, but let's check again. Wait, maybe I made a mistake. Wait, \(3\frac{1}{6}\) yards for \(1\frac{1}{3}\) shirts. So fabric per shirt is \(3\frac{1}{6}\div1\frac{1}{3}\). \(3\frac{1}{6}=\frac{19}{6}\), \(1\frac{1}{3}=\frac{4}{3}\). So \(\frac{19}{6}\div\frac{4}{3}=\frac{19}{6}\times\frac{3}{4}=\frac{19}{8}=2\frac{3}{8}\)? Wait no, \(\frac{19}{8}\) is \(2\frac{3}{8}\)? Wait no, 19 divided by 8 is 2 with remainder 3, so \(2\frac{3}{8}\). Then for 2 shirts, it's \(2\frac{3}{8}\times2\)? Wait no, wait the question is: the store has \(3\frac{1}{6}\) yards for \(1\frac{1}{3}\) shirts. She wants to make 2 shirts. So first, find how much fabric is needed for 1 shirt, then multiply by 2. Wait, maybe my first step was wrong. Let's re - do:

\(3\frac{1}{6}\) yards for \(1\frac{1}{3}\) shirts. So fabric per shirt: \(3\frac{1}{6}\div1\frac{1}{3}=\frac{19}{6}\div\frac{4}{3}=\frac{19}{6}\times\frac{3}{4}=\frac{19}{8}\) yards per shirt. Then for 2 shirts: \(\frac{19}{8}\times2=\frac{19}{4}=4\frac{3}{4}\) yards. But let's check the options. Option A is \(4\frac{3}{4}\) yards. Wait, but let's check the calculation again.

Wait, \(3\frac{1}{6}=\frac{19}{6}\), \(1\frac{1}{3}=\frac{4}{3}\). Dividing \(\frac{19}{6}\) by \(\frac{4}{3}\) is \(\frac{19}{6}\times\frac{3}{4}=\frac{19\times3}{6\times4}=\frac{57}{24}=\frac{19}{8}=2\frac{3}{8}\) yards per shirt? Wait no, that's per shirt? Wait, no: \(1\frac{1}{3}\) shirts use \(3\frac{1}{6}\) yards. So per shirt is total fabric divided by number of shirts. So \(3\frac{1}{6}\) yards / \(1\frac{1}{3}\) shirts. So \(\frac{19}{6}\div\frac{4}{3}=\frac{19}{6}\times\frac{3}{4}=\frac{19}{8}=2\frac{3}{8}\) yards per shirt. Then for 2 shirts: \(2\frac{3}{8}\times2=\frac{19}{8}\times2=\frac{19}{4}=4\frac{3}{4}\) yards. So option A is \(4\frac{3}{4}\) yards.

Answer:

A. \(4\frac{3}{4}\) yards