Final answer:
The correct answer is option c. 2x + 5y + 3z = 172, 5x + y + 8z = 269, x + 4y + z = 74. This system of equations can be used to determine the sale price of the sweaters, shirts, and pants.
Step-by-step explanation:
The correct answer is option c. 2x + 5y + 3z = 172, 5x + y + 8z = 269, x + 4y + z = 74
To determine the sale price of the sweaters, shirts, and pants using the given purchase scenarios, we must establish a system of linear equations that corresponds to each scenario. The first equation, 2x + 5y + 3z = 172, represents the cost of 2 sweaters, 5 shirts, and 3 pairs of pants totaling $172. The second equation, 5x + 8z = 269, represents the cost of 5 sweaters and 8 pairs of pants totaling $269. Finally, the third equation, 4y + z = 74, represents the cost of 4 shirts and 1 pair of pants totaling $74. These equations align with the quantities of each item purchased and the total cost reported for those items.
To determine the sale price of the sweaters, shirts, and pants, we need a system of equations that represents the given information. Let x represent the number of sweaters, y represent the number of shirts, and z represent the number of pants.
From the given information, we can create the following equations:
- 2x + 5y + 3z = 172 (equation 1)
- 5x + 8z = 269 (equation 2)
- x + 4y + z = 74 (equation 3)
These three equations form a system that can be used to determine the sale price of the sweaters, shirts, and pants.