Answer:
Option A - x + y = 531 , y = 2x
Explanation:
Given : The variable x represents the number of long sleeve shirts Nancy bought.
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.
To find : How many of each type of shirt did she buy
Solution : From the given statements we conclude that,
Statement 1 - 'Nancy bought 531 shirts for her business'.
..........[1]
Statement 2 - 'She bought 2 times as many short sleeve shirts as long sleeve shirts'.
..........[2]
These two equation form the system of equation model of above problem
→
..........[1] and
→
..........[2]
Now, we solve equation [1] and [2],
Put the value of y from equation [2] into [1],
........[3]
Put value of x in [2],
......[4]
The equation [3] and [4] shows the solution of the system
Long sleeve shirts = 177
Short sleeve shirts = 354
And total = 531
Therefore, Option A is correct - x + y = 531 , y = 2x
Therefore, the number of long sleeve shirts Nancy bought is 177 and the number of short sleeve shirts she bought is 354.
Also, the system of equations models this problem are:
and which is the last option in the given set of options.