Seven hundred gallons of 91-octane gasoline is obtained by mixing 87-octane gasoline with 94-octane gasoline.Write a system of equations in which one equation represents the amount of final mixture required and the other represents the amounts of 87- and 94-octane gasolines in the final mixture.Let x and y represent the numbers of gallons of 87-octane and 94-octane gasolines,respectively.
A) $$\left\{ \begin{array} { c }
x + y = 85 \
87 x + 94 y = 63,700
\end{array} \right.$$
B) $$\left\{ \begin{array} { c }
87 x + 94 y = 700 \
x + y = 85
\end{array} \right.$$
C) $$\left\{ \begin{array} { l }
x + y = 63,700 \
87 x + 94 y = 85
\end{array} \right.$$
D) $$\left\{ \begin{array} { c }
87 x + 94 y = 700 \
x + y = 63,700
\end{array} \right.$$
E) $$\left\{ \begin{array} { c }
x + y = 700 \
87 x + 94 y = 63,700
\end{array} \right.$$

Question

Seven hundred gallons of 91-octane gasoline is obtained by mixing 87-octane gasoline with 94-octane gasoline.Write a system of equations in which one equation represents the amount of final mixture required and the other represents the amounts of 87- and 94-octane gasolines in the final mixture.Let x and y represent the numbers of gallons of 87-octane and 94-octane gasolines,respectively. ​
A)​ $$\left\{ \begin{array} { c } 
x + y = 85 \
87 x + 94 y = 63,700
\end{array} \right.$$
B)​ $$\left\{ \begin{array} { c } 
87 x + 94 y = 700 \
x + y = 85
\end{array} \right.$$
C)​ $$\left\{ \begin{array} { l } 
x + y = 63,700 \
87 x + 94 y = 85
\end{array} \right.$$
D)​ $$\left\{ \begin{array} { c } 
87 x + 94 y = 700 \
x + y = 63,700
\end{array} \right.$$
E)​ $$\left\{ \begin{array} { c } 
x + y = 700 \
87 x + 94 y = 63,700
\end{array} \right.$$

Quizplus · Accepted Answer

The first equation, $x + y = 700$, represents the total amount of gasoline in gallons, which is the sum of the gallons of 87-octane and 94-octane gasolines. The second equation, $87x + 94y = 63,700$, represents the total octane level of the mixture, calculated by multiplying the gallons of each type of gasoline by its octane rating and setting it equal to the total octane level of the final mixture (700 gallons of 91-octane gasoline).

Seven Hundred Gallons of 91-Octane Gasoline Is Obtained by Mixing {x+y=8587x+94y=63,700\left\{ \begin{array} { c } x + y = 85 \\87 x + 94 y = 63,700\end{array} \right.{x+y=8587x+94y=63,700​

Seven Hundred Gallons of 91-Octane Gasoline Is Obtained by Mixing $\left\{ \begin{array} { c } x + y = 85 \\87 x + 94 y = 63,700\end{array} \right.$