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  1. Every sunny day, a plant increases in weight by 5 grams. On days which are not sunny the
    plant decreases in weight by 3 grams. Over a total of 16 days, overall
    the plant increased in
    weight by 8 grams. How many sunny days were there? [2]
    ​

Verified Answer :

sitapoudellamichhane

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.

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