Question

Ethan, Caleb, and Jayden went to a bakery to buy desserts. Ethan bought 2 cupcakes, 2

brownies and a pie for $20. Caleb bought 4 cupcakes, 4 brownies and a pie for $44, Jayden
bought 5 cupcakes and 6 brownies for $40. Write a system of equations to represent is
situation. Convert the system to a matrix and find the cost of 1 cupcake, 1 brownie, and 1
pie to the nearest cent.

Answer 1

x = 32

y = -20 and

z = -4

Explanation:

Cupcakes = X

Brownies = Y

Pies = Z

Ethan = 2x+2y+z = 20

Caleb = 4x+4y+z = 44

Jayden = 5x+6y = 40

-1(2x+2y+z=20) =

(-2x - 2y - z = -40) + (4x+4y+z=44)

= 5x + 6y = 40

-3(2x+2y=24 =

(-6 - 6y = -72) + (5x + 6y = 40)

= - x = - 32

= x = 32

5 (32) + 6y = 40

= 160 + 6y = 40

6y = 40 - 160

y = 120/6

y = - 20

2(32) + 2(-20) + z = 20

64 - 40 + z = 20

z = 20 - 24

z = -4