project 1 A

Description

(Must show all work & break it down)
Project Question A: percentages

This set of questions will explore the effect of applying two or more percentages to a value.

1) (A% increase and B% decrease)
You find a pair of shoes that have an original price of $145. Suppose the shoes are on sale for 15% off, and suppose there is also a sales tax of 8.5%.
a) Calculate the total price you pay at the register if you first take 15% off, and then add on the 8.5% sales tax. Show all work clearly.
b) Calculate the total price you pay at the register if you first add on the 8.5% sales tax, and then add in the 15% discount. Show all work clearly.
c) In general, if you increase a number by A%, and also decrease the number by B%, does the order in which you perform the increase/decrease matter?

2) (A% decrease and B% decrease)
Everything in a store is 25% off. You also have a coupon for an additional 30% off the price of one item.
a) Pick a starting price and calculate the total final price you would pay at the register if you first take 25% off, and then take the 30% off. Show all work clearly.
b) Re-do your calculation from part (a), but this time take the 30% off first, and then take the 25% off. Show all work to clearly show how to calculate the final price.
c) Does it matter which way you perform the calculation?
d) In general, if you decrease a number by A%, and also decrease the number by B%, does the order in which you perform the decrease matter?

3) (A% increase and B% increase compared to (A+B)% increase)
Suppose I start a job at a salary of $120,000 per year. I get a raise of 4% the second year, and then I get a 6% raise the third year.
a) Calculate my salary after getting the two raises. Show all work clearly.
b) Calculate my salary if I had instead gotten one 10% raise (instead of getting a 4% raise followed by a 6% raise).
c) If I get a 4% raise followed by a 6% raise, is my resulting salary the same as getting one 10% raise?
d) In general, if you increase a number by A%, and then increase that by B%, will you get the same final answer is just doing one increase of (A+B)%?

4) (A% decrease followed by $B decrease vs. $B decrease followed by A% decrease)
Suppose you purchase an item that has an original price of $300. Everything in the store is 30% off. You also have a coupon for an additional $12 off.
a) Calculate the total price you pay at the register if you first take 30% off, and then you use the $12 off coupon. Show all work clearly.
b) Calculate the total price you pay at the register if you do the calculation from part (a) the other way around.
c) In general, if you do an A% decrease followed by a B DOLLAR decrease, will you get the same final answer as first doing the B DOLLAR decrease followed by an A% decrease?

5) Suppose you initially invest $12,000 in the stock market. Suppose the value of your investment decreases by 14% in the first year.
a) How much money is your investment now worth at the end of the first year? Show all work.
b) By what percentage would the account need to increase during the second year in order to bring the value back up to $12,000 by the end of the second year? Show all work clearly.

6) Suppose I invest $1,200 in the stock market. Suppose the value of the investment decreased by 20% during the first year, and then the account gained 20% during the second year. How much would the account be worth at the end of the second year? Show all work clearly.