Question 1202013
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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
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<pre>
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 = {{{(1544*8-1472*14)/(10*8-18*14)}}} = 48 dollars

    cost a dozen of t-sweatshirt y = {{{(10*1472-18*1544)/(10*8-18*14)}}} = 76 dollars
</pre>

Solved.


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On the determinant method &nbsp;(= the Cramer's rule) &nbsp;for &nbsp;2 &nbsp;equations in &nbsp;2 &nbsp;unknowns see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-using-det.lesson>Solution of the linear system of two equations in two unknowns using determinant</A> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/What-is-a-matrix.lesson>What is a matrix?</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Determinant-of-a-2x2-matrix.lesson>Determinant of a 2x2-matrix</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/HOW-TO-solve-system-of-linear-eqns-in-two-unknowns-using-det.lesson>HOW TO solve system of linear equations in two unknowns using determinant (Cramer's rule)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-systems-of-linear-equations-in-two-unknowns-using-Cramer%27s-rule.lesson>Solving systems of linear equations in two unknowns using the Cramer's rule</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-word-problems-by-reducing-them-to-systems-of-linear-equations-in-two-unknowns.lesson>Solving word problems by the Cramer's rule after reducing to systems of linear equations in two unknowns</A>  

in this site.