A coffee blend contains Sumatra beans that cost $5/lb and Kona beans that cost $13/lb. If the blend costs $10/lb, how much of each type of coffee is in 50 lb of the blend?

Question

anonymous · Answer

lets introduce a variable, say $x$ is the number of pounds of Kona, so since the total is 50 there must be $50-x$ pounds of Sumatra
then you are going to end up with 50 pounds of $10 blend for a total of $50\times\$ 10=\$500$

the $x$ pounds of Kona cost $13x$ and the $50-x$ pounds of Sumatra cost $\$5(50-x)$ for a total of $13x+5(50-x)$
since you know the total is 500 set 
$$13x+5(50-x)=500$$ and solve for $x$

anonymous · Answer

if you are used to solving these as a system of equations you would write 
$$x+y=50$$
$$13x+5y=500$$ but you would then solve for $y$ in the first equation and get $y=50-x$ substitute in to the second equation and get 
$$13x+5(50-x)=500$$ so there is really no difference in method