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3rd Test - Percents
1) What is 30% of 200? ______60______
If 30% of 100 is 30, then 30% of 200 is 60.
About 1/3 of the students got this problem correct (more than any other question).
2) There were 40 questions on the test. Joe got 3 wrong. What percent did he get correct? ___92.5%____
There are 40 questions so each one is worth 100/40 = 2.5%
Another way to look at it is to find (40-3)/40 = 37/40= x/100, x= 100* 37/40 = 370/4 = 92.5%
I gave half credit if you guessed and were between 88% and 95%
3) What is 20% of 20% of 125? _____5_____
20% is the same as 1/5
1/5 of 1/5 of 125 = 125/ 5 / 5 = 25/ 5 = 5
4) What percent of 80 is 20? ____25%_____
This is the same as asking what is 20/80 in percentage terms?
You should know that 1/4 is the same as 25%
Common wrong answers were 40% and 4.
5) 49 is 70% of what number? ____70_____
70/100 x = 49?
100 * 49 / 70 = 10 * 49/7 = 10 * 7 = 70
6) You are a helper an expedition that finds $20 million in pirate treasure. The leader has stated that he gets 60% and the rest will be split among the 10 helpers (of which you are one). What is your cut of the loot? $800,000
If the leader take 60% for himself, that leaves only $8 million to split among 10 helpers.
That means you get $800,000. One person wrote 4% an I accepted that too.
7) If Sabrina earns $150 a day, and her boss just increased her salary to $165 a day, by what percentage was her salary increased? ______10%______
I did not give any partial credit on this one because I though it was relatively easy.
10% of 150 is 15. So 150 + 15 = 156. The salary increase was 10%
More people had 15% as an answer than had 10%.
8) Duncan sold 50% of his DVDs plus 1/2 a DVD to Veronica. He then sold 50% of what was left plus half a DVD to Pat. He has three DVDs left. How many DVDs did he have originally? ___15 DVDs__
This is very much like the yugi-oh problem we had during team competition earlier.
All the people who had 13 as their answer probably did not verify it.
Try working backwards. Starting with 3, figure out how many he had before the last transaction.
The only number that works is 7 because 50% of 7 is 3.5. 3.5 + 1.2 = 4.
Then for the transaction before that he must have had 15 because 50% of 15 is 7.5 + 1/2 = 8.
Finally verify your answer: 15 - (7.5 + 1/2) = 7 - (3.5 + 1/2) = 3
9) If you flipped a set of 3 pennies 1000 times, estimate how many of those thousand times do you think all three pennies would come up heads? ____125______
I'm glad to see that a lot of people realized that they should expect fewer than half the trials to
come up all heads. For and away the most popular answer was 333, but I only gave 1/5 credit for that.
Think of the 8 different ways that 3 pennies can land. All heads is just one of those 8 ways.
In terms of probability the chance of getting all heads is 1/2 * 1/2 * 1/2 = 1/8
1/8 * 1000 = 125. Only one person got this exactly right
If you don't believe the answer is 125 try running this dice simulation I wrote in java.
Select 3 dice with 2 sides each (to simulate 3 pennies) from the options.
10) If you put $100 in the bank, and it earns 20% interest each year, estimate how much will you have after 10 years? (Keep in mind that the interest is compounded each year) _____$619_____
I wrote on the board that compounded means that interest is computed based on the original
amount plus all the interest earned so far.
This means that after the first year you will have $120 and
after the second year you will have $131 and
after the third year you will have $143.1 and
:
after the tenth year you will have $619.17 (full credit for $600-$650)
Another way to do it is 100 (1.2)^10 = 619.17
If 30% of 100 is 30, then 30% of 200 is 60.
About 1/3 of the students got this problem correct (more than any other question).
2) There were 40 questions on the test. Joe got 3 wrong. What percent did he get correct? ___92.5%____
There are 40 questions so each one is worth 100/40 = 2.5%
Another way to look at it is to find (40-3)/40 = 37/40= x/100, x= 100* 37/40 = 370/4 = 92.5%
I gave half credit if you guessed and were between 88% and 95%
3) What is 20% of 20% of 125? _____5_____
20% is the same as 1/5
1/5 of 1/5 of 125 = 125/ 5 / 5 = 25/ 5 = 5
4) What percent of 80 is 20? ____25%_____
This is the same as asking what is 20/80 in percentage terms?
You should know that 1/4 is the same as 25%
Common wrong answers were 40% and 4.
5) 49 is 70% of what number? ____70_____
70/100 x = 49?
100 * 49 / 70 = 10 * 49/7 = 10 * 7 = 70
6) You are a helper an expedition that finds $20 million in pirate treasure. The leader has stated that he gets 60% and the rest will be split among the 10 helpers (of which you are one). What is your cut of the loot? $800,000
If the leader take 60% for himself, that leaves only $8 million to split among 10 helpers.
That means you get $800,000. One person wrote 4% an I accepted that too.
7) If Sabrina earns $150 a day, and her boss just increased her salary to $165 a day, by what percentage was her salary increased? ______10%______
I did not give any partial credit on this one because I though it was relatively easy.
10% of 150 is 15. So 150 + 15 = 156. The salary increase was 10%
More people had 15% as an answer than had 10%.
8) Duncan sold 50% of his DVDs plus 1/2 a DVD to Veronica. He then sold 50% of what was left plus half a DVD to Pat. He has three DVDs left. How many DVDs did he have originally? ___15 DVDs__
This is very much like the yugi-oh problem we had during team competition earlier.
All the people who had 13 as their answer probably did not verify it.
Try working backwards. Starting with 3, figure out how many he had before the last transaction.
The only number that works is 7 because 50% of 7 is 3.5. 3.5 + 1.2 = 4.
Then for the transaction before that he must have had 15 because 50% of 15 is 7.5 + 1/2 = 8.
Finally verify your answer: 15 - (7.5 + 1/2) = 7 - (3.5 + 1/2) = 3
9) If you flipped a set of 3 pennies 1000 times, estimate how many of those thousand times do you think all three pennies would come up heads? ____125______
I'm glad to see that a lot of people realized that they should expect fewer than half the trials to
come up all heads. For and away the most popular answer was 333, but I only gave 1/5 credit for that.
Think of the 8 different ways that 3 pennies can land. All heads is just one of those 8 ways.
In terms of probability the chance of getting all heads is 1/2 * 1/2 * 1/2 = 1/8
1/8 * 1000 = 125. Only one person got this exactly right
If you don't believe the answer is 125 try running this dice simulation I wrote in java.
Select 3 dice with 2 sides each (to simulate 3 pennies) from the options.
10) If you put $100 in the bank, and it earns 20% interest each year, estimate how much will you have after 10 years? (Keep in mind that the interest is compounded each year) _____$619_____
I wrote on the board that compounded means that interest is computed based on the original
amount plus all the interest earned so far.
This means that after the first year you will have $120 and
after the second year you will have $131 and
after the third year you will have $143.1 and
:
after the tenth year you will have $619.17 (full credit for $600-$650)
Another way to do it is 100 (1.2)^10 = 619.17