Question

Find the cost for each pound of jelly beans and each pound of almonds

Answer 1

Let 'x' represent the cost for each pound of jelly beans.

Let 'y' represent the cost for each pound of almonds.

For the first statement, the mathematical expression is

$\begin{gathered} 9x+7y=37\ldots\ldots1 \\ \end{gathered}$

For the second statement, the mathematical expression is,

$3x+5y=17\ldots\ldots2$

Combining the two equations

$\begin{gathered} 9x+7y=37\ldots\ldots\text{.}.1 \\ 3x+5y=17\ldots\ldots2 \end{gathered}$

Applying the elimination method to resolve the systems of equation

Multiply the second equation by 3, in order to eliminate x

$\begin{gathered} 9x+7y=37\ldots\ldots\ldots1 \\ 3x+5y=17\ldots\ldots\ldots2\times3 \end{gathered}$$\begin{gathered} 9x+7y=37\ldots\ldots\text{.}.1 \\ 9x+15y=51\ldots\ldots2 \end{gathered}$

Subtract equation 1 from 2

$\begin{gathered} 9x-9x+15y-7y=51-37 \\ 8y=14 \\ \frac{8y}{8}=\frac{14}{8} \\ y=\frac{7}{4}=1.75 \\ \therefore y=1.75 \end{gathered}$

Substitute y = 1.75 into equation 1 in order to solve for x

$\begin{gathered} 9x+7y=37 \\ 9x+7(1.75)=37 \\ 9x+12.25=37 \\ 9x=37-12.25 \\ 9x=24.75 \\ \frac{9x}{9}=\frac{24.75}{9} \\ x=2.75 \end{gathered}$

Hence, the cost for each pound of jelly beans = x = $2.75.

the cost for each pound of almonds = y = $1.75.