High School

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A box contains a total of 12 cookies and muffins. Cookies cost $3.00 each, and muffins cost $2.00 each. The total cost of the box is $32.00. Let [tex]x[/tex] represent the number of cookies and [tex]y[/tex] the number of muffins. Write a system of linear equations to find the number of cookies and muffins in the box.

Answer :

Final answer:

To determine the number of cookies and muffins in the box, set up a system of linear equations using the total number of items (x + y = 12) and the total cost (3x + 2y = 32) to solve for x and y.

Explanation:

To find the number of cookies and muffins in a box using the given information, we can set up a system of linear equations.

Step 1:

Define the variables:

Let x represent the number of cookies.

Let y represent the number of muffins.

Step 2:

Write the equations based on the given information:

The box contains a total of 12 items: x + y = 12 (Equation 1)

The cost of the items totals $32, with cookies costing $3 each and muffins costing $2 each: 3x + 2y = 32 (Equation 2)

These two equations form the system that can be solved to find the quantities of cookies and muffins in the box.

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