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PERCENT OF A NUMBER Lesson 28 Section 2 To find the Base We have seen (Lesson 27) that finding the Amount involves multiplication. To find 3% of $600, where $600 is the Base, first name 1%: 1% of $600 is $6.00. Therefore, 3% is 3 × $6.00 = $18.00. But say that we are given $18.00, and we ask: $18.00 is 3% of how much? In other words, 3 × ? = $18.00? To find the Base, then, we have to divide. $18 ÷ 3 = $6. But $6 is 1% of the Base. The Base itself is 100 times that. $18 is 3% of $600. And we could check that. 1% of $600 is $6.00. So 3% is 3 × $6.00 = $18.00. |
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Example 1. $36 is 4% of how much? Answer. The Base -- the number that follows "of" -- is missing. And $36 ÷ 4 = $9 But $9 is 1% of the Base. The Base itself is 100 times that. $36 is 4% of $900. Let's check that. 1% of $900 is $9. Therefore, 4% is 4 × $9 = $36.
Example 2. 42 is 6% of what number? Check the answer. Answer. 42 ÷ 6 = 7; times 100 = 700. Here is the check: 1% of 700 = 7. Therefore, 6% = 6 × 7 = 42. Example 3. 8% of what number is 20?
20 is 8% of 250. Check: 1% of 250 = 2.5
Answer. The problem asks: 14 is two thirds of what number? But if 14 is two thirds, then half of 14 is one third. Half of 14 is 7. And 7 is one third -- of 21.
Example 5. 30 is 60% -- three fifths -- of what number? Answer. If 30 is three fifths of some number, then a third of 30 is one fifth. A third of 30 is 10. And 10 is one fifth -- of 50. Example 6. 24 is 150% of what number?
the formal method (Lesson 25, Example 8): 24 is 150% of -- 1½ times -- 16. (16 + 8 = 24.) Thus, if the Amount is more than 100% of a number -- 24 is 150% of 16 -- then that number will be less than the Amount. Therefore, multiply the Amount by the reciprocal of the fractional form of the percent. Example 7. 36 is 225% of what number?
Example 8. Maria is retired and withdraws money from her retirement account. But a tax of 20% is automatically withheld. If she needs $1200, how much must she actually request? Solution. Since 20% will be withheld, Maria will receive 80% of her request. So the question is: $1200 is 80% of how much?
request one and a quarter times, or one quarter more, than what she actually needs. One quarter of $1200 is $300. Therefore she must withdraw $1500. It is then a simple matter to see that 20%, or one fifth, of $1500 is $300, so that her net amount will in fact be $1200. Please "turn" the page and do some Problems. or Introduction | Home | Table of Contents Please make a donation to keep TheMathPage online. Copyright © 2001-2007 Lawrence Spector Questions or comments? E-mail: themathpage@nyc.rr.com |