Question 1182899
.
A baker purchased 13 lb of wheat flour and 10 lb of rye flour for a total cost of $14.10. 
A second purchase, at the same prices, included 15 lb of wheat flour and 14 lb of rye flour. 
The cost of the second purchase was $17.50. 
Find the cost per pound of the wheat flour and of the rye flour.
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<pre>
Let  x  be the price per pound of the wheat and 

let  y  be the price per pound of the rye flour.


Write the system of two equations as you read the problem


    13x + 10y = 14.10    (1)

    15x + 14y = 17.50    (2)



Use the determinant method to solve the system (the same as the Cramer's rule).



The determinant of the coefficient matrix is  D = 13*14 - 15*10 = 32.



The determinant to find the unknown x is      Dx = 14.10*14 - 17.50*10 = 22.4;

    so  x = {{{(Dx)/D}}} = {{{22.4/32}}} = 0.7  dollars.



The determinant to find the unknown y is      Dy = 13*17.50 - 15*14.10 = 16;

    so  y = {{{Dy/D}}} = {{{16/32}}} = 0.5  dollars.


<U>ANSWER</U>.  The prices are  $0.7  for pound of wheat and  $0.5 for pound of rye flour.
</pre>

Solved.


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On Cramer's rule for solving systems of 2 equations in 2 unknowns see the lessons

&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.


Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic 
&nbsp;&nbsp;&nbsp;&nbsp; "<U>2x2-Matrices, determinants, Cramer's rule for systems in two unknowns</U>"