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If the weight of a package is multiplied by 5/7 the result is 40.5 pounds. What is the weight of the package?

Mar 30, 2016

$56.7 \textcolor{w h i t e}{i} \text{pounds}$

Explanation:

$1$. Start by making a "let statement."

Let $x$ represent the weight of the package.

$2$. Create an algebraic expression.

$\frac{5}{7} x = 40.5 \textcolor{w h i t e}{i} \text{pounds}$

$3$. Isolate for $x$ by dividing both sides by $\frac{5}{7}$.

$\frac{5}{7} x \div \frac{5}{7} = 40.5 \textcolor{w h i t e}{i} \text{pounds} \div \frac{5}{7}$

$4$. Recall that in order to divide a fraction by another fraction, take the reciprocal of the divisor and change the division sign to a multiplication sign.

$\frac{5}{7} x \cdot \frac{7}{5} = 40.5 \textcolor{w h i t e}{i} \text{pounds} \cdot \frac{7}{5}$

$5$. Solve for $x$.

$\frac{5 \cdot 7}{7 \cdot 5} x = \frac{40.5 \cdot 7}{5} \textcolor{w h i t e}{i} \text{pounds}$

$x = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} 56.7 \textcolor{w h i t e}{i} \text{pounds} \textcolor{w h i t e}{\frac{a}{a}} |}}}$