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Mindy and Troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake and Troy had [tex]\(\frac{1}{4}\)[/tex] of the total cake.

1. Write an equation to determine how many pieces of cake [tex]\((c)\)[/tex] there were in total.
[tex]\[
\square
\][/tex]

2. Find the total number of pieces of cake.
[tex]\[
\square \text{ pieces of cake}
\][/tex]

Sagot :

GinnyAnsweridn
Let's start by defining the variables and setting up the equation based on the information given:

- 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] pieces.

We are told that Mindy and Troy combined ate 9 pieces of cake. Thus, we can write the following equation:

[tex]\[ 3 + \frac{1}{4}c = 9 \][/tex]

Now, let's solve this equation step-by-step to find the total number of pieces of cake, [tex]\( c \)[/tex].

1. Start by isolating the term with [tex]\( c \)[/tex]. Subtract 3 from both sides of the equation:

[tex]\[ \frac{1}{4}c = 9 - 3 \][/tex]

2. Simplify the right side:

[tex]\[ \frac{1}{4}c = 6 \][/tex]

3. To isolate [tex]\( c \)[/tex], multiply both sides of the equation by 4:

[tex]\[ c = 6 \times 4 \][/tex]

4. Perform the multiplication:

[tex]\[ c = 24 \][/tex]

So, the total number of pieces of cake is [tex]\( \boxed{24} \)[/tex].
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