Let's approach this problem by determining how many dishes the new menu has. The new menu has \(20\%\) more dishes than the previous menu, and the previous menu had \(D\) dishes.
First, let's calculate the increase in the number of dishes:
[tex]\[ 20\% \text{ of } D = \frac{20}{100} \times D = 0.2D \][/tex]
Now, to find the total number of dishes on the new menu, we add this increase to the original number of dishes \(D\):
[tex]\[ D + 0.2D = 1.2D \][/tex]
So, the new menu has \(1.2D\) dishes.
Next, we need to determine which of the given expressions correctly represent this number of dishes.
Let's examine each option:
Option A: \(20D\)
- This expression suggests the number of dishes is 20 times the number of previous dishes. This is clearly not correct as the increase should only be \(20\%\), not 2000\%.
Option B: \(D + 20D\)
- Simplifying this, we get:
[tex]\[ D + 20D = 21D \][/tex]
Like Option A, this is much more than the \(20\%\) increase that we need. Thus, this is incorrect.
Option C: \(1.2D\)
- This expression directly represents the new number of dishes after a \(20\%\) increase from \(D\):
[tex]\[ 1.2D \][/tex]
It matches our calculated value perfectly. This option is correct.
Option DD: \(D + 20\)
- This expression suggests the number of dishes is the original number plus 20. This would only be accurate if \(D\) were equal to 100 dishes originally, which is not necessarily the case. Thus, this is incorrect.
Option E: \(D + \frac{1}{5}D\)
- Let's simplify this:
[tex]\[ D + \frac{1}{5}D = D + 0.2D = 1.2D \][/tex]
This is identical to our earlier calculation. Hence, this option is also correct.
Thus, the correct expressions that represent how many dishes Crispy Clover's new menu has are:
(C) [tex]\(1.2D\)[/tex] and (E) [tex]\(D + \frac{1}{5}D\)[/tex].
