#### Answer

Three apples and two avocados must be taken to get 1000 calories and 100 grams of carbohydrates.

#### Work Step by Step

Let us assume the number of apples be x and the number of avocados be y that need to be taken to have 1000 calories and 100 grams of carbohydrates.
So, the equation becomes:
$100x+350y=1000$
Also, we know that the carbohydrates contained by one apple and one avocado are $24$ and $14$:
$24x+14y=100$
Then, multiply, the equation $24x+14y=100$ by 25,
$600x+350y=2500$
And subtract $100x+350y=1000$ from $600x+350y=2500,$
$\begin{align}
& 500x=1500 \\
& x=3
\end{align}$
Put x = 3 in $24x+14y=100$,
$\begin{align}
& 24\times 3+14y=100 \\
& 14y=100-72 \\
& 14y=28 \\
& y=2
\end{align}$
So, $ x=3,y=2$.
Hence, three apples and two avocados must be taken to get 1000 calories and 100 grams of carbohydrates.