A coffee manufacturer sells a 14-pound package that contains three flavors of coffee for $25.French vanilla coffee costs $5 per pound,hazelnut flavored coffee costs $5.50 per pound,and Swiss chocolate flavored coffee costs $6 per pound.The package contains the same amount of hazelnut as Swiss chocolate.Let f represent the number of pounds of French vanilla,h represent the number of pounds of hazelnut,and s represent the number of pounds of Swiss chocolate.
Write a system of linear equations that represents the situation.

A) $$\left\{ \begin{array} { c l }
5 f - 5.5 h + 6 s & = 25 \
f + h + s & = 14 \
h - s & = 0
\end{array} \right.$$
B) $$\left\{ \begin{aligned}
5 f + 5.5 h + 6 s & = 25 \
f + h + s & = 14 \
h - s & = 0
\end{aligned} \right.$$
C) $$\left\{ \begin{array} { c l }
5 f - 5.5 h + 6 s & = 25 \
f - h + s & = 14 \
h - s & = 0
\end{array} \right.$$
D) $$\left\{ \begin{array} { c l }
5 f - 5.5 h + 6 s & = 25 \
f + h + s & = 14 \
h + s & = 0
\end{array} \right.$$
E) $$\left\{ \begin{array} { c l }
5 f - 5.5 h - 6 s & = 25 \
f - h - s & = 14 \
h + s & = 0
\end{array} \right.$$

Question

A coffee manufacturer sells a 14-pound package that contains three flavors of coffee for $25.French vanilla coffee costs $5 per pound,hazelnut flavored coffee costs $5.50 per pound,and Swiss chocolate flavored coffee costs $6 per pound.The package contains the same amount of hazelnut as Swiss chocolate.Let f represent the number of pounds of French vanilla,h represent the number of pounds of hazelnut,and s represent the number of pounds of Swiss chocolate. ​
Write a system of linear equations that represents the situation.
​
A) $$\left\{ \begin{array} { c l } 
5 f - 5.5 h + 6 s & = 25 \
f + h + s & = 14 \
h - s & = 0
\end{array} \right.$$ ​
B)​ $$\left\{ \begin{aligned}
5 f + 5.5 h + 6 s & = 25 \
f + h + s & = 14 \
h - s & = 0
\end{aligned} \right.$$
C)​ $$\left\{ \begin{array} { c l } 
5 f - 5.5 h + 6 s & = 25 \
f - h + s & = 14 \
h - s & = 0
\end{array} \right.$$
D)​ $$\left\{ \begin{array} { c l } 
5 f - 5.5 h + 6 s & = 25 \
f + h + s & = 14 \
h + s & = 0
\end{array} \right.$$
E)​ $$\left\{ \begin{array} { c l } 
5 f - 5.5 h - 6 s & = 25 \
f - h - s & = 14 \
h + s & = 0
\end{array} \right.$$

Quizplus · Accepted Answer

We want to find a system of linear equations that represents the situation. 
Let f represent the number of pounds of French vanilla coffee, h represent the number of pounds of hazelnut flavored coffee, and s represent the number of pounds of Swiss chocolate flavored coffee. 
- The package contains 14 pounds of coffee, so f + h + s = 14 
- The package costs $25, so 5f + 5.5h + 6s = 25 
- The amount of hazelnut coffee is the same as the amount of Swiss chocolate coffee, so h = s 
Therefore, the system of linear equations is:

f + h + s = 14 
5f + 5.5h + 6s = 25 
h = s

The best choice is B because it correctly represents the situation and includes all three variables with their given values and relationships.

A Coffee Manufacturer Sells a 14-Pound Package That Contains Three {5f−5.5h+6s=25f+h+s=14h−s=0\left\{ \begin{array} { c l } 5 f - 5.5 h + 6 s & = 25 \\f + h + s & = 14 \\h - s & = 0\end{array} \right.⎩⎨⎧​5f−5.5h+6sf+h+sh−s​=25=14=0​

A Coffee Manufacturer Sells a 14-Pound Package That Contains Three $\left\{ \begin{array} { c l } 5 f - 5.5 h + 6 s & = 25 \\f + h + s & = 14 \\h - s & = 0\end{array} \right.$