Sure, let's work through the problem step by step.
1. Initial Value:
Let's denote the initial value by \( x \).
2. Increased by 50%:
When \( x \) is increased by 50%, we calculate the new value as follows:
[tex]\[
x + 0.50x = 1.50x
\][/tex]
3. Decreased by 30%:
Now, we take the increased value \( 1.50x \) and decrease it by 30%. To do this, we multiply \( 1.50x \) by \( (1 - 0.30) \):
[tex]\[
1.50x \times (1 - 0.30) = 1.50x \times 0.70
\][/tex]
Simplifying the multiplication:
[tex]\[
1.50 \times 0.70 = 1.05
\][/tex]
So the resultant expression is:
[tex]\[
1.05x
\][/tex]
Therefore, if [tex]\( x \)[/tex] is increased by 50% and then decreased by 30%, the resulting value is [tex]\( 1.05x \)[/tex].
