Question

Cory, Josh and Dan went shopping for Halloween treats. Cory bought 3 chocolate pumpkins, 4 masks and 8 candy witches. He spent $36.65. Josh bought 5 chocolate pumpkins,3 masks and 10 candy witches. He spent $37.50. Dan bought 4 chocolate pumpkins, 5 masks and 6 candy witches. He spent $43.45. Write a system of equations to represent this problem.

Answer 1

Answer:

$\left\{\begin{matrix}3x+4y+8z=36.65\\ 5x+3y+10z=37.50\\ 4x+5y+6z=43.35\end{matrix}\right.$

Step-by-step explanation:

System of equations

Let's set the following variables:

x=Price of chocolate pumpkins

y=Price of masks

z=Price of candy witches

We'll establish the system of equations needed to know the prices of all the Halloween treats.

Cory bought 3 chocolate pumpkins, 4 masks, and 8 candy witches and he spent $36.65. This leads to the following equation:

$3x+4y+8z=36.65\qquad\qquad [1]$

Josh bought 5 chocolate pumpkins, 3 masks, and 10 candy witches and he spent $37.50. This leads to the following equation:

$5x+3y+10z=37.50\qquad\qquad [2]$

Dan bought 4 chocolate pumpkins, 5 masks, and 6 candy witches and he spent $43.45. This leads to the following equation:

$4x+5y+6z=43.35\qquad\qquad [3]$

Collecting the equations [1] [2] [3], we form the system of equations to represent this problem:

$\left\{\begin{matrix}3x+4y+8z=36.65\\ 5x+3y+10z=37.50\\ 4x+5y+6z=43.35\end{matrix}\right.$