If y is decreased by `20%` and then increased by `60%`, what is the new number, expressed in terms of y?

Answer

To solve the problem step by step, we will first decrease the value of \( y \) by \( 20\% \) and then increase the result by \( 60\% \).

### Step 1: Decrease \( y \) by \( 20\% \)

To find \( 20\% \) of \( y \), we calculate:
\[ 20\% \text{ of } y = \frac{20}{100} \times y = 0.2y \]
Now, we subtract this from \( y \):
\[ \text{New value after decrease} = y - 0.2y = 0.8y \]

### Step 2: Increase the new value by \( 60\% \)

Next, we need to increase \( 0.8y \) by \( 60\% \). First, we calculate \( 60\% \) of \( 0.8y \):
\[ 60\% \text{ of } 0.8y = \frac{60}{100} \times 0.8y = 0.6 \times 0.8y = 0.48y \]
Now, we add this to \( 0.8y \):
\[ \text{New value after increase} = 0.8y + 0.48y = 1.28y \]

### Final Answer

The new number, expressed in terms of \( y \), is:
\[ \boxed{1.28y} \]