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?

Question

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