<PRE><B>Question 121454</B>
At Gwen&#39;s garage sale, all books were one price, and all magazines were another price. harriet bought four books and three magazines for $1.45 and June bought two books and five magazines for $1.25. What was the price of a book and what was the price for a magazine?&lt;br&gt;&lt;br&gt;

This problem is solved using a system of linear equations using eliminaiton.  First off we need to set up the variables.&lt;br&gt;

x = price of each book
y = price of each magazine&lt;br&gt;

now we set up our system&lt;br&gt;

4x + 3y = 1.45
2x + 5y = 1.25&lt;br&gt;

now we multiply by 100 to clear the decimals&lt;br&gt;

400x + 300y = 145
200x + 500y = 125&lt;br&gt;

Now multiply the second equation by -2.&lt;br&gt;

-400x - 1000y = -250&lt;br&gt;

Now add the first equation to that and cancel the x&#39;s and solve for y.&lt;br&gt;

400x + 300y = 145
-400x - 1000y = -250
---------------------
-700y = -105
y = 0.15&lt;br&gt;

now plug that into the first equation and solve for x.&lt;br&gt;

400x + 300(0.15) = 145
400x + 45 = 145
400x = 100
x = 0.25&lt;br&gt;

So each book is priced at 25 cents and each magazine is priced at 15 cents.  </PRE>