Question

Miss Croft made snack bags for the picnic that contain three types of snacks: packages of crackers, packages of cookies, and candy bars. A snack bag containing 6 of each type of snack costs $21.00. A snack bag containing 8 packages of crackers, 5 packages of cookies, and 10 candy bars costs $26.00. A snack bag containing 5 packages of crackers, 4 packages of cookies, and 7 candy bars costs $18.50. If x represents packages of crackers, y represents packages of cookies, and z represents candy bars, construct a system of equations that can be used to determine the price of each snack.

Answer 1

Let´s represent the problem's variables by the following letters:

X : PACKAGES OF CRACKERS

Y: PACKAGES OF COOKIES

Z : CANDY BARS

Then we have the following linear system

First linear equation: A snack bag containing 6 of each type of snack costs $21.00.

6X + 6Y + 6 Z = 21

Second linear equation: . A snack bag containing 8 packages of crackers, 5 packages of cookies, and 10 candy bars costs $26.00

8X + 5Y + 10 Z = 26

THIRD LINEAR EQUATION: A snack bag containing 5 packages of crackers, 4 packages of cookies, and 7 candy bars costs $18.50.

5X + 4Y + 7Z = 18.50

So the system of equations that can be used to determine the price of each snack is:

6X + 6Y + 6 Z = 21

8X + 5Y + 10 Z = 26

5X + 4Y + 7Z = 18.50