In a certain clothing store, 6 shirts and 3 ties cost $79.50, and 3 shirts and 2 ties cost $41. Determine the cost of each tie.

veraguitars1234 Feb 13, 2020

#1**+2 **

Let x be the cost of a shirt and y be the cost of a tie.....so....we have this system of equations :

6x + 3y = 79.50

3x + 2y = 41

Multiply the second equation through by -2 and we have

6x + 3y = 79.50

-6x - 4y = -82 add these

-y= -2.5

y= 2.5 = $2.50 = the cost of a tie

And using 3x + 2y =41 we can find the cost of a shirt

3x + 2(2.50) = 41

3x + 5 = 41 subtract 5 from both sides

3x = 36 divide both sides by 3

x = $12 = the cost of a shirt

CPhill Feb 13, 2020

#2**+1 **

Let's make s the price for a shirt.

And t the price of a tie:

6s + 3t = 79.50

3s + 2t = 41.

We can modify the equation by multiplying the second one by -2.

-6s - 4t = -82.

Solving for t: **t = 2.5.**

Solving for s:

Knowing t, we can solve the equation:

3s + 2(2.50) = 41. (I'm using this one because it's easier)

3s + 5 = 41

3s = 36

**s = 12**

**t = 2.5**

I didn't really know the answer, until I looked at CPhill's, and now I understand the solution and how to do it now. Thanks CPhill!!

AnimalMaster Feb 13, 2020