Algebra-2

To find out how many of each type of pastry box Mark should buy, let's set up the equations based on the given information.

Variables

1.Let ( x ) be the number of cookie boxes.

2.Let ( y ) be the number of cupcake boxes.

3.Let ( z ) be the number of cake boxes.

Given Information

The total number of pastry boxes is 120:

x + y + z = 120 (Equation 1)

The total cost must not exceed $1,800:

10x + 15y + 20z = 1800 (Equation 2)

Mark wants to buy twice as many cupcake boxes as cookie boxes:

y = 2x (Equation 3)

Substitute Equation 3 into Equations 1 and 2

Substituting ( y = 2x ) into Equations 1 and 2:

Substituting into Equation 1:

x + 2x + z = 120
3x + z = 120 (Equation 4)

Substituting into Equation 2:

10x + 15(2x) + 20z = 1800

10x + 30x + 20z = 1800

40x + 20z = 1800(Equation 5)

Now we have a new s...