Question

the value of a painting increased by 179% from the end of 2017 to the end of 2018 and then decreased by 27% from the end of 2018 to the end of 2019. what was the net percentage increase in the value of the painting from the end of 2017 to the end of 2019?

Explanation:

Step1: Let the initial value be \( V \) (end of 2017).

After a 179% increase in 2018, the value becomes \( V(1 + \frac{179}{100}) = V(2.79) \).

Step2: Then, decrease this value by 27% in 2019.

The new value is \( V(2.79)(1 - \frac{27}{100}) = V(2.79)(0.73) \).
Calculate \( 2.79\times0.73 \):
\( 2.79\times0.73 = 2.0367 \)
So the value at the end of 2019 is \( 2.0367V \).

Step3: Find the net percentage increase.

The increase from \( V \) to \( 2.0367V \) is \( (2.0367 - 1)\times100\% = 103.67\% \).

Answer:

The net percentage increase is \( 103.67\% \)