Algebra 2 word problem

Harvey’s expresso express, a drive through coffer stop, is famous for its great house coffee,

a blend of Colombian and mocha java beans.

Their archrival, JoJo’s java, sent a spy to steal their ratio for blending beans.

The spy returned with a torn part of an old receipt that showed only the total number of pounds and the total cost, 18 pounds for $92.07.

At first JoJo was angry, but then he realized that he knew the price per pound of each kind of coffee

($4.89 for Colombian and $5.43 for mocha java).

Show how he could use equations to figure out how many pounds of each type of beans Harvey’s used.

Let x = pounds of Colombian coffee
Let y = pounds of mocha jave coffee

$\begin{array}{|rcll|} \hline x + y &=& 18\ \text{pounds} \qquad \text{ or } \qquad x= 18\ \text{pounds} - y\\ x\cdot \dfrac{$4.89}{\text{1 pound}} + y\cdot \dfrac{$5.43}{\text{1 pound}} &=& $92.07 \\ \hline \end{array}$

$\begin{array}{|rcll|} \hline 4.89x+5.43y&=& 92.07 \quad &| \quad x = 18 - y \\ 4.89\cdot (18 - y) + 5.43y&=& 92.07 \\ 4.89\cdot18 -4.89y + 5.43y&=& 92.07 \\ 88.02 + 0.54y&=& 92.07 \quad &| \quad -88.02 \\ 0.54y&=& 92.07 -88.02 \\ 0.54y&=& 4.05 \quad &| \quad : 0.54 \\ y&=& \frac{4.05}{ 0.54 } \\ \mathbf{y}&\mathbf{=}& \mathbf{7.5\ \text{pounds } } \\\\ x &=& 18-y \\ x &=& 18 - 7.5 \\ \mathbf{x} &\mathbf{=}& \mathbf{10.5\ \text{pounds }} \\ \hline \end{array}$

Harvey’s used 10.5 pounds of Colombian coffee and 7.5 pounds of mocha jave coffee