Answer:
7 sunny days
Explanation:
Let's denote the number of sunny days as \( x \) and the number of non-sunny days as \( y \). We know the following:
1. Each sunny day increases the weight by 5 grams, so the total weight increase from sunny days is \( 5x \) grams.
2. Each non-sunny day decreases the weight by 3 grams, so the total weight decrease from non-sunny days is \( -3y \) grams.
3. The total increase over 16 days is 8 grams, so \( 5x - 3y = 8 \).
4. The total number of days is 16, so \( x + y = 16 \).
We have a system of two equations:
\[ 5x - 3y = 8 \]
\[ x + y = 16 \]
We can solve this system of equations to find \( x \) and \( y \).
From the second equation, we can express \( y \) in terms of \( x \):
\[ y = 16 - x \]
Substitute this into the first equation:
\[ 5x - 3(16 - x) = 8 \]
\[ 5x - 48 + 3x = 8 \]
\[ 8x - 48 = 8 \]
\[ 8x = 56 \]
\[ x = 7 \]
So, there were 7 sunny days.