Correct Answers to 8th Grade percentage test

A-Successive Discounts: Three Paragraphs, please,

You are working at a store and a customer presents you with two coupons for discounts, one for 20% and one for 30%. The customer doesn’t understand why this doesn’t translate into a discount of 50% for a purchase of $100. You explain that it is your store’s policy that you must apply discounts consecutively and not simultaneously.
a. Does it matter which order you take the discounts? Why/why not?

It does not matter in which order you take the discount 20% and 30% off. This is because you will end up getting the same price for a $100 item. For example, if you take 30% off first and then 20%, you will find $70 and then $56 (since 20% of $70 is $14). If you take 20% off first and then 30%, you will find $80, and then $56 (since 30% of $80 is $24). Either way, the same result is obtained.

b. Is this a coincidence for 20 and 30%? What if the coupons were 10 and 50%?

This is not just a fluke for 20 and 30% because it works with other percentages. For example, if you take 10% off first and then 50%, you will find $50 and then $45 (since 10% of 50 is 5). This proves that the order that the discounts are taken (which does not matter) is not a coincidence for 20 and 30%.

c. Can you take this problem to the next step and explain how to calculate the successive discount result of any two percentages. You can develop your own formula or equation.

To calculate the successive discount result for any two percentages, one must first calculate the result with one of the percentages (it does not matter which one) and using the result obtained, calculate the final result with the other percentage. For example, if you wanted to calculate the successive discount result of a $1,000 purchase with the percentages of 20 and 10%, you would first subtract 20% of $1,000 (although 10% is also an option) which would lead to $800. Then you would subtract 10% of $800, which would lead to the final result of $720 (since 10% of $800 is $80).

B-Wholesale/Retail: Three paragraphs, please.

a. You are working at a store where the price paid by the store (the wholesale cost of items) is marked up (increased) by 100%, i.e. doubled. What percent discount off the selling price of the items (retail price) will result in the store “breaking even” (incurring neither profit not loss on the sale of the item)? Use a $100 item as an example.

A discount of 50% off the retail price will result in the store breaking even. Using a $100 item as an aexample, it is bought by the store for $100 and then marked up 100%. That means the retail price of the item is $200. For the store to break even, it would have to offer a 50% discount on this item because the store would receive $100 when it is sold (since 50% of $200 is $100).

b. What if the mark up had been 150%? Ditto.

A discount of 60% of the retail price will result in the store breaking even. Using a $100 item as an example, it is bought by the store for $100 ad then marked up 150%. That means the retail price of the item is $250. For the store to break even, it would have to offer a 60% discount on this item so that it is sold for $100 (because 60% of $250 is $150 and 250-150=100).

c. What if the mark up had been 200%? Ditto.

A discount of 66⅔% of the retail price will result in the store breaking even. Using a $100 item as an example, it is bought by the store for $100 and then marked up 200%. That means that the retail price of the item is $300. For the store to break even, it would have to offer a 66⅔% discount on this item so that it is sold for $100 (because 66⅔% of $300 is $200 and 300-200=100).


C- My investment story: Three paragraphs, please.

In October, 2007 I moved my retirement savings into a market index fund. The Dow Jones was about 14,000 points. From the moment I made this move, the Dow moved fairly steadily down, until March, 2009, when it hit about 7,000 points. Yesterday it hit 10,000 poits for the first time in 2009.

a. What percent had it decreased from when I invested until this past March?

The Dow Jones had decreased 50% from when you invested it until this past March. This is because 7,000 is 50% of 14,000 and 14,000-7,000=7,000. So the total decrease of the Dow Jones was 50%.

b. What percent had it increased from March until yesterday?

The Dow Jones had increased 42.9% from March until yesterday. This is because 3,000 is 42.9% of 7,000 and 7,000+3,000=10,000. So the decrease of the Dow Jones was 42.9%.

c. What percent had it changed from October, 2007 until yesterday?

The Dow Jones had decreased 28.6% from October, 2007 until yesterday. This is because 4,000 is 28.6% of 14,000 and 14,000-4,000=10,000. So the Dow Jones decreased 28.6% from October 2077 until yesterday.