Question

Gooey Goods, a gourmet cookie store, sells chocolate chip cookies for $15 a dozen and brownies for $18 a dozen. How many of each baked good should be combined to create a party tray with 6 dozen treats that sells for $96?
Write your answers as whole numbers, decimals, or simplified fractions or mixed numbers. Do not round.
dozen chocolate chip cookies
dozen brownies

Answer 1

To solve the problem, we can set up a system of equations based on the information provided.

Let:
- \( x \) = the number of dozen chocolate chip cookies
- \( y \) = the number of dozen brownies

From the information given, we can formulate the following equations:

1. The total number of dozen treats must equal 6:
\[
x + y = 6
\]

2. The total cost of the treats must equal $96:
\[
15x + 18y = 96
\]

Now we have a system of equations to solve.

### Step 1: Solve the first equation for \( y \)
From the first equation:
\[
y = 6 - x
\]

### Step 2: Substitute \( y \) into the second equation
Now substitute \( y \) in the second equation:
\[
15x + 18(6 - x) = 96
\]

### Step 3: Expand and simplify
Expanding the equation, we get:
\[
15x + 108 - 18x = 96
\]
Combine like terms:
\[
-3x + 108 = 96
\]

### Step 4: Solve for \( x \)
Now, isolate \( x \):
\[
-3x = 96 - 108
\]
\[
-3x = -12
\]
\[
x = \frac{-12}{-3} = 4
\]

### Step 5: Solve for \( y \)
Using the value of \( x \) in the first equation to find \( y \):
\[
y = 6 - x = 6 - 4 = 2
\]

### Conclusion
Thus, the solution is:
- \( x = 4 \) dozen chocolate chip cookies
- \( y = 2 \) dozen brownies

The final answers are:
- **4 dozen chocolate chip cookies**
- **2 dozen brownies**