Question 933361
<p>First, break down what they are saying and write all statements as equations:<br /><br /><br />1. There are two types of seats: $25 ones and $50 dollar ones. Assign variables for these types of seats<br /><br /><br />X = $25 seats, Y = $42 seats<br /><br /><br />2. The amount of seats sold (number of tickets) is 50.<br /><br /><br />X + Y = 50<br /><br /><br />3. Total money raised is $1590.<br /><br /><br />25X + 42Y = 1590 ($25*number of X seats PLUS $42*number of Y seats = total amount of money made)<br /><br /><br />This is a system of equations. Since you have 2 unknowns you need two equations to solve them, and that is what we have:<br /><br /><br />X + Y = 50<br />25X + 42Y = 1590<br /><br /><br />Isolate any variable from one equation, and insert it into the other:<br /><br /><br />X = 50 - Y&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; [isolating X in first equation]<br />25(50-Y) + 42Y = 1590&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; [inserting it into second equation]<br />1250 - 25Y + 42Y = 1590&nbsp; &nbsp;&nbsp; [solving for Y]<br />17Y = 340<br />Y = 20<br /><br /><br />So 20 of the $42 seats were sold. Now put that answer into either equation to find how many $25 seats were sold (X seats).<br /><br /><br />X + 20 = 50<br />X = 30<br /><br /><br />To Check:<br /><br /><br />20+30 does equal 50 and:<br /><br /><br />25(30) + 20(42) = 1590 ???<br />750 + 840 = 1590 ???<br />1590 = 1590&nbsp; YES<br /><br /><br />Hope that helps :)<br /><br /><br /></p>