Given:
The cost of one pound from Costa Rican = $9.30
The cost of one pound from Organic free trade = $12.80
It is required to make 50 pounds by mixing the two types to make a new coffee
which the cost of the pound will be = $12.45
so, let the number of pounds from Costa Rican = x
And the number of pounds from Organic Free Trade = y
So, we can write the following system of equations:
[tex]\begin{gathered} x+y=50\rightarrow(1) \\ 9.30x+12.80y=12.45\cdot50\rightarrow(2) \end{gathered}[/tex]
Form equation (1)
[tex]x=50-y\rightarrow(3)[/tex]
substitute with (x) from equation (3) into equation (2)
[tex]9.30\cdot(50-y)+12.80y=12.45\cdot50[/tex]
solve the equation to find (y):
[tex]\begin{gathered} 9.30\cdot50-9.30y+12.80y=12.45\cdot50 \\ 465+3.5y=622.5 \\ 3.5y=622.5-465 \\ 3.5y=157.5 \\ y=\frac{157.5}{3.5}=45 \end{gathered}[/tex]
substitute with (y) into equation (3) to find (x):
[tex]x=50-45=5[/tex]
So, the answer will be:
5 pounds of Costa Rican coffee
45 pounds of Organic Free trade coffee
