Q45. - Algebra 1

Question

Find the number of band uniforms that can be made with $\mathbf{131}\frac{\mathbf{3}}{\mathbf{4}}$ yards of fabric if each uniform requires $\mathbf{3}\frac{\mathbf{7}}{\mathbf{8}}$ yards.

Step-by-Step Solution

Answer

Bands of uniform pieces can be made with $131\frac{3}{4}$ yards of fabric if each uniform requires $3\frac{7}{8}$ yards.

Step 1. Convert mixed fraction to proper fraction.

Mixed fractions of $131\frac{3}{4}$ yards and $3\frac{7}{8}$ yards can be converted into proper fractions as shown below by simplifying,

$\begin{array}{c}131\frac{3}{4} \mathrm{yards}=\frac{\left(131\right)\left(4\right)+3}{4}\mathrm{yards}\\ =\frac{527}{4}\mathrm{yards}\\ 3\frac{7}{8} \mathrm{yards}=\frac{\left(3\right)\left(8\right)+7}{8}\mathrm{yards}\\ =\frac{31}{8}\mathrm{yards}\end{array}$

Step 2. Divide 131 3 4 yards by 3 7 8 yards

The number of band uniforms that can be made with $131\frac{3}{4}$ yards of fabric if each uniform requires $3\frac{7}{8}$ yards will be evaluated when $131\frac{3}{4}$ is divided by $3\frac{7}{8}$. Therefore,

$\begin{array}{c}131\frac{3}{4}÷3\frac{7}{8}=\left(\frac{527}{4}\right)÷\left(\frac{31}{8}\right)\\ =\frac{527}{4}\times \frac{8}{31}\\ =34\end{array}$

Step 3. Description of step.

Band of uniforms can be made with $131\frac{3}{4}$ yards of fabric if each uniform requires $3\frac{7}{8}$ yards.