Question

A department store sells yellow and purple shirts. Each yellow shirt is the same price. Each purple shirt is the same price. However, the price of yellow shirts is different from the price of purple shirts.

On Monday, the store collected $165 selling 5 purple shirts and 7 yellow shirts.

On Tuesday, the store collected $213 selling 4 purple shirts and 11 yellow shirts.

What is the cost of each shirt? Graph the point that represents the cost of each shirt. The provided line on the graph represents Tuesday's sales.

Answer 1

Each purple shirt costs $12

Each yellow shirt costs $15

Explanation:

Let's call:

x: purple shirt price (in dollars per shirt)

y: yellow shirt price (in dollars per shirt)

On Monday, the store collected $165 selling 5 purple shirts and 7 yellow shirts. That is:

5*x + 7*y = 165 (eq. 1)

On Tuesday, the store collected $213 selling 4 purple shirts and 11 yellow shirts. That is:

4*x+11*y = 213 (eq. 2)

We can isolate y in equation 1, as follows:

7*y = 165 - 5*x

y = 165/7 - 5/7*x

and replace it in equation 2:

4*x+11*(165/7 - 5/7*x) = 213

4*x+ 1815/7 - 55/7*x = 213

-27/7*x = 213 - 1815/7

-27/7*x = -324/7

x = -324/-27 = 12

Then:

y = 165/7 - 5/7*12 = 15

If we graph the system of equations made by equations 1 and 2, we get the figure attached. The intersection of the two lines is the solution of the system.

Answer 2

The Cost of yellow shirts is $15 and the cost of purple shirt is $ 60

Explanation:

Let cost of one yellow shirt be x

and the cost of one purple shirt be y

On Monday

5x + 7y = 165--------------------(1)

On Tuesday

4x + 11y = 213----------------------(2)

To solve (1) and (2)

multiplying eq(1) with 4

20x + 28y = 660--------------------(3)

multiplying eq(2) with 5

20x + 55y = 1056-------------------(4)

Subtracting (3) from (4)

20x + 55y = 1056

20x + 28y = 660

(-)

-----------------------------------

0x +27y = 405

-----------------------------------

`y = (405)/(27)`

y = 15

Substituting y value in eq(1)

5x + 7(15) = 165

5x + 105 =405

5x =405 -105

5x =300

x = \frac{300}{5}

x =60