Lesson Percentage Word Problems (discount)
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<html><body>A typical word problem involving percentages might look something like this: Ned got a <font color="#330099">12%</font> discount when he bought his new jacket. If the original price, before the discount, was <font color="#330099">$50</font>, how much was <font color="#330099">the discount</font>? Word problems tend to be even wordier than this one. The solution process involves making the problem simpler and simpler, until it's a math problem with no words. Step 1. Identify what they're asking for, and call it x. <font color="#330099">x</font> = amount of the discount. Step 2. Use the information given to write an equation that relates the <font color="#330099">quantities</font> involved. 12% of 50 dollars = the amount of the discount (x). Step 3. Translate into Math:</br></br>(12/100) * 50 = x. Step 4. Solve for x:</br></br>6 = x. This means that Ned's 12% off amounted to a $6 discount. A few examples of some word problems using this method are in the table below. You can <a href="http://www.mathick.com/mathick.php?topic=percentages">try a sample problem</a> if you'd like to practice and see if you're doing it correctly. <center><table border = '1'><tr><td>Problems:</td><td> </td><td><tt><font color='#000000' size='5'><font color = 'blue'>A. The original price was $160, and Ned got a 20% discount? How much was the discount?</font> <font color = 'red'>B. The original price was $90, and Ned got a $36 discount. How many percent off was the discount?</font> <font color = 'green'>C. Ned's discount was 20% off the original price, which meant a $40 discount. What was the original price?</font></font></tt></td></tr><tr></tr><tr><td>Write an equation:</td><td> </td><td><tt><font color='#000000' size='5'><font color = 'blue'>A. What is 20% of 160?</font> <font color = 'red'>B. 36 is what percent of 90?</font> <font color = 'green'>C. 40 is 20% of what number?</font></font></tt></td></tr><tr></tr><tr><td>Translate into math: is = “=” of = “*” What = “x” 5% = “5/100”, etc. </td><td> </td><td><tt><font size='5'><font color = 'blue'>A.</font> <table border = '1''><tr> <td><font color = 'blue'>What </font></td> <td><font color = 'blue'>is </font></td> <td><center><font color = 'blue'>20%</font></center></td> <td><font color = 'blue'>of </font></td> <td><font color = 'blue'>160?</font></td></tr><tr> <td><font color = 'blue'>x </font></td> <td><font color = 'blue'>= </font></td> <td><font color = 'blue'>(20/100)</font></td> <td><font color = 'blue'> * </font></td> <td><font color = 'blue'>160.</font></td></tr></table></br><font color = 'red'>B. <table border = '1'><tr> <td><font color = 'red'>36 </font></td> <td><font color = 'red'>is </font></td> <td><center><font color = 'red'>what %</font></center></td> <td><font color = 'red'>of </font></td> <td><font color = 'red'>90?</font></td></tr><tr> <td><font color = 'red'>36 </font></td> <td><font color = 'red'>= </font></td> <td><font color = 'red'>(x/100)</font></td> <td><font color = 'red'> * </font></td> <td><font color = 'red'>90.</font></td></tr></table></font></br><font color = 'green'>C. <table border = '1'><tr> <td><font color = 'green'>40 </font></td> <td><font color = 'green'>is </font></td> <td><center><font color = 'green'>20%</font></center></td> <td><font color = 'green'>of </font></td> <td><font color = 'green'>what number?</font></td></tr><tr> <td><font color = 'green'>40 </font></td> <td><font color = 'green'>= </font></td> <td><font color = 'green'>(20/100)</font></td> <td><font color = 'green'> * </font></td> <td><font color = 'green'>x.</font></td></tr></table></font></br></font></tt></td></tr><tr></tr><tr><td>Simplify & solve for x:</br>(This may involve solving a linear equation - click <a href="http://www.mathick.com/mathick.php?topic=lineq1">here</a> to practice.)</td><td> </td><td><tt><font color='#000000' size='5'><font color = 'blue'>A. x = (.2)*160, so x = 32</font> <font color = 'red'>B. 36 = (.9)x, so x = 40</font> <font color = 'green'>C. 40 = (.2)x, so x = 200</font></font></tt></td></tr><tr></tr></table></center></body></html>
