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# 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.

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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.

Feb 13, 2020

#1
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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

Feb 13, 2020
#2
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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!!

Feb 13, 2020