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Which system of equations models this problem?


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?

Ax + y = 531

y = 2x

Bx - y = 531

y = 2x

Cx + 2y = 531

y = 2x

Dx + y = 2

y = 531x

Verified Answer :

HomertheGenius

We know that Nancy bought 531 shirts. The variable x represents the number of long sleeve shirts and y represents the number of short sleeve shirts.Therefore:x + y = 531"She bought 2 times as many short sleeve shirts (y) as long sleeve shirts (x)."y = 2 xAnswer:A.  x + y = 531y = 2 x

Answer:

Option A -  x + y = 531  , y = 2x

Step-by-step 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'.

\(x+y = 531\) ..........[1]

Statement 2 - 'She bought 2 times as many short sleeve shirts as long sleeve shirts'.

\(y = 2x\) ..........[2]

These two equation form the system of equation model of above problem

→ \(x+y = 531\) ..........[1] and

→ \(y = 2x\) ..........[2]

Now, we solve equation [1] and [2],

Put the value of y from equation [2] into [1],

\(x+2x = 531\)

\(3x = 531\)

\(x = 177\) ........[3]

Put value of x in [2],

\(y = 2(177)=354\) ......[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.



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