Question

The variable x represents the number of long-sleeve shirts Nancy bought and the variable y represents the number of short-sleeve shirts she bought. Nancy bought 531 shirts for her business. She bought 2 times as many short-sleeve shirts as long-sleeve shirts. How many of each type of shirt did she buy? Which system of equations models this problem?

1) A system of equations: Row 1: x + y = 531, Row 2: y = 2x
2) A system of equations: Row 1: x + 8y = 531, Row 2: y = 8x
3) A system of equations: Row 1: x - y = 531, Row 2: y = 2x
4) A system of equations: Row 1: x + y = 2, Row 2: y = 531x

Answer 1

The correct system of equations that models the number of shirts Nancy bought for her business is x + y = 531 and y = 2x. By solving this system, we determine that Nancy bought 177 long-sleeve shirts and 354 short-sleeve shirts.

Step-by-step explanation:

The question asks us to determine how many long-sleeve shirts (x) and short-sleeve shirts (y) Nancy bought for her business if the total number of shirts is 531 and she bought twice as many short-sleeve shirts. To model this scenario with a system of equations, we use two equations. The first equation represents the total number of shirts bought, which is the sum of long-sleeve and short-sleeve shirts: x + y = 531. The second equation represents the relationship between the number of short-sleeve shirts and long-sleeve shirts: y = 2x. Therefore, the correct system of equations that models this problem is:

• Row 1: x + y = 531
• Row 2: y = 2x

To solve the system, we can substitute the second equation into the first to find the value of x:

• x + 2x = 531
• 3x = 531
• x = 531 / 3
• x = 177

Using the value of x, we can find y:

• y = 2(177)
• y = 354

Nancy bought 177 long-sleeve shirts and 354 short-sleeve shirts.