A department store sells yellow and purple shirts. Each yellow shirt is the same price. Each purple shirt is the same price. How

Question

3 years ago

12

A department store sells yellow and purple shirts. Each yellow shirt is the same price. Each purple shirt is the same price. How

ever, 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.

Mathematics

2 answers:

lana [24] · Answer 1 · 2022-09-02T03:58:35+03:00

Answer:

Each purple shirt costs $12

Each yellow shirt costs $15

Step-by-step 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.