SOLUTION: a company sells two custom T-shirt and sweatshirt packages. one package contains 10 dozen t-shirts and 14 dozen sweatshirts for $1544. the other package contains 18 dozen T-shirts

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Question 1202013: a company sells two custom T-shirt and sweatshirt packages. one package contains 10 dozen t-shirts and 14 dozen sweatshirts for $1544. the other package contains 18 dozen T-shirts and 8 dozen sweatshirts for $1472. find the cost of a dozen t-shirts and a dozen sweatshirts
Found 3 solutions by josgarithmetic, mananth, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(t,p) for t-shirt price per dozen, sweatshirt price per dozen

Points described are (10,14) and (18,8).

Two described cost equations are
system%2810t%2B14p=1544%2Cand%2C18t%2B8p=1472%29

Simplify and solve the system.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
a company sells two custom T-shirt and sweatshirt packages. one package contains 10 dozen t-shirts and 14 dozen sweatshirts for $1544. the other package contains 18 dozen T-shirts and 8 dozen sweatshirts for $1472. find the cost of a dozen t-shirts and a dozen sweatshirts
Assume
$ x Price of one dozen T shirts
$ y Price of one dozen sweat shirts

Package 1
10 x + 14.00 y = 1544.00...............1

Package 2
18 x + 8.00 y = 1472.00 .............2
Eliminate y
multiply (1)by -8
Multiply (2) by 14
-80 x -112 y = -12352.00
252 x 112 y = 20608.00
Add the two equations
172.00 x = 8256.00

/ 172.00
x = 48.00
plug value of x in (1)
10.00 x + 14.00 y = 1544.00
480.00 + 14.00 y = 1544.00
14.00 y = 1064.00
y = 76.00
Ans x = 48
y = 76
$ 48.00 Price of one dozen T shirts
$ 76.00 Price of one dozen sweat shirts

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
a company sells two custom T-shirt and sweatshirt packages.
one package contains 10 dozen t-shirts and 14 dozen sweatshirts for $1544.
the other package contains 18 dozen T-shirts and 8 dozen sweatshirts for $1472.
find the cost of a dozen t-shirts and a dozen sweatshirts
~~~~~~~~~~~~~~~~~ 

Let x = the cost of a dozen of t-shirts
    y = the cost of a dozen of sweatshirts


Write equations as you read the problem

    10x + 14y = 1544  dollars   (1)
    18x +  8y = 1472  dollars   (2)


Next apply the determinant methos of solution and get the answers

    cost a dozen of t-shirt      x = %281544%2A8-1472%2A14%29%2F%2810%2A8-18%2A14%29 = 48 dollars

    cost a dozen of t-sweatshirt y = %2810%2A1472-18%2A1544%29%2F%2810%2A8-18%2A14%29 = 76 dollars

Solved.

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On the determinant method  (= the Cramer's rule)  for  2  equations in  2  unknowns see the lessons
    - Solution of the linear system of two equations in two unknowns using determinant

    - What is a matrix?
    - Determinant of a 2x2-matrix
    - HOW TO solve system of linear equations in two unknowns using determinant (Cramer's rule)
    - Solving systems of linear equations in two unknowns using the Cramer's rule
    - Solving word problems by the Cramer's rule after reducing to systems of linear equations in two unknowns
in this site.