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 .

STEP 1
x= cost of shirt
y= cost of tie

Set up two equations (one for each store), then solve for one variable by using the elimination method (or whichever method you are comfortable with).

FIRST STORE EQUATION
6x + 3y= $79.50

SECOND STORE EQUATION
3x + 2y= $41.00

STEP 2
Solve by elimination; multiply second equation by -2 to eliminate the x term and solve for y.

multiply second equation by -2
(-2)(3x + 2y)= (-2)($41.00)
-6x - 4y= -82.00

add first equation and multiplied second equation together
6x + 3y= 79.50
-6x - 4y= -82.00
x term cancels out

-y= -2.50
divide both sides by -1

y= $2.50 per tie

STEP 3
substitute y value in either original equation to solve for x

6x + 3y= 79.50
6x + 3(2.50)= 79.50

6x + 7.50= 79.50
subtract 7.50 from both sides

6x= 72.00
divide both sides by 6

x= $12.00 per shirt

CHECK
using opposite original equation as step 3

3x + 2y= $41.00
3(12.00) + 2(2.50)= 41.00
36.00 + 5.00= 41.00
41.00= 41.00

ANSWER: Each shirt costs $12.00 and each tie costs $2.50.

Hops this helps! :)