Answer
$3$ apples
$2$ avocados
Work Step by Step
Let's note:
$x$=the number of apples
$y$=the number of avocados
We can write the system of equations:
$\begin{cases}
100x+350y=1000\\
24x+14y=100
\end{cases}$
Simplify:
$\begin{cases}
50(2x+7y)=1000\\
2(12x+7y)=100
\end{cases}$
$\begin{cases}
2x+7y=20\\
12x+7y=50
\end{cases}$
Use the addition method: multiply Equation 1 by -1 and add it to Equation 2 to eliminate $y$ and determine $x$:
$\begin{cases}
-2x-7y=-20\\
12x+7y=50
\end{cases}$
$-2x-7y+12x+7y=-20+50$
$10x=30$
$x=3$
Substitute the value of $x$ in Equation 1 to find $y$:
$2x+7y=20$
$2(3)+7y=20$
$6+7y=20$
$7y=20-6$
$7y=14$
$y=2$
The system's solution is:
$x=3$ apples
$y=2$ avocados
