Question

1. tyler bought 8 boxes of donuts to bring to school. some boxes contained 8 chocolate donuts, and the rest contained 6 glazed donuts. he bought 52 donuts in all. how many boxes of glazed donuts did he buy? write and solve a system of equations (2 equations) that represent the problem.

Explanation:

Step1: Define variables

Let \( x \) be the number of boxes of chocolate donuts and \( y \) be the number of boxes of glazed donuts.

Step2: First equation (total boxes)

The total number of boxes is 8, so \( x + y = 8 \).

Step3: Second equation (total donuts)

Each chocolate box has 8 donuts and each glazed box has 6 donuts, and total donuts are 52. So \( 8x + 6y = 52 \).

Step4: Solve the system

From the first equation, \( x = 8 - y \). Substitute into the second equation:
\( 8(8 - y) + 6y = 52 \)
\( 64 - 8y + 6y = 52 \)
\( 64 - 2y = 52 \)
\( -2y = 52 - 64 \)
\( -2y = -12 \)
\( y = 6 \)

Answer:

The number of boxes of glazed donuts Tyler bought is 6. The system of equations is \(

$$\begin{cases} x + y = 8 \\ 8x + 6y = 52 \end{cases}$$

\) and the solution for \( y \) (glazed boxes) is 6.