To determine the total number of pieces of cake, let's follow these steps:
1. Define the Variables:
- Let [tex]\( c \)[/tex] be the total number of pieces of cake.
- Mindy ate 3 pieces of cake.
- Troy ate [tex]\(\frac{1}{4}\)[/tex] of the total cake, which is [tex]\(\frac{1}{4}c\)[/tex].
2. Set Up the Equation:
Since the combined total number of pieces eaten by Mindy and Troy is 9, we can write the following equation:
[tex]\[
3 + \frac{1}{4}c = 9
\][/tex]
3. Solve the Equation:
- First, isolate [tex]\(\frac{1}{4}c\)[/tex] by subtracting 3 from both sides of the equation:
[tex]\[
\frac{1}{4}c = 9 - 3
\][/tex]
[tex]\[
\frac{1}{4}c = 6
\][/tex]
- Next, solve for [tex]\(c\)[/tex] by multiplying both sides of the equation by 4:
[tex]\[
c = 6 \times 4
\][/tex]
[tex]\[
c = 24
\][/tex]
Therefore, the total number of pieces of cake is [tex]\( \boxed{24} \)[/tex].
