Two word problems Composite and Inverse Fractions

[smbroadb]

Please help, I am very confused on how to go about doing these two problems.

1. Traders often buy foreign currency in hope of making money when the currency's value changes. For example, on July 6, 2011, one U.S. dollar could purchase 0.6985 Euros and one Euro could purchase 1.3822 Canadian dollars. Let f(x) represent the number of Euros you can buy with x dollars and let g(x) represent the number of Canadian dollars you can buy with x Euros.

a. Find a function that relates dollars to Euros

b. Find a function that relates Euros to Canadian Dollars.

c. Then use the results of a) and b) to find a function that relates U.S. Dollars to Canadian Dollars.



2. You make a purchase at a local store, but what you've bought is too big to take home in your car. For a small fee, you arrange to have the store deliver your purchase. You pay for your purchase, plus the sales tax, plus the fee. The tax rate is 8.5% and the delivery fee is $30.

a. Write a function P(x) for the total, including taxes, on the purchase amount x.

b. Write a function T(x) for the total, including the delivery fee, on the purchase amount x.

c. Calculate and interpret (P*T)(x) and (T*P)(x). Which results in a lower cost to you?

If someone would be able to help me with these two problems it would be greatly appreciated! Thank you!

[maggiemagnet]

1. Traders often buy foreign currency in hope of making money when the currency's value changes. For example, on July 6, 2011, one U.S. dollar could purchase 0.6985 Euros and one Euro could purchase 1.3822 Canadian dollars. Let f(x) represent the number of Euros you can buy with x dollars and let g(x) represent the number of Canadian dollars you can buy with x Euros.
a. Find a function that relates dollars to Euros

You are given that "x" stands for "number of dollars" and "f(x)" stands for "number of Euros". You are given that each dollar buys 0.6985 Euros. If you have 1 dollar, how many Euros is that? If you have 2 dollars, how many Euros is that? If you have 3 dollars, how many Euros is that? Using the same process as you used to answer those questions: If you have x dollars, how many Euros is that? Use your translating skills to convert this relationship into a function.

b. Find a function that relates Euros to Canadian Dollars.

This part works the same way as part (a) does.

c. Then use the results of a) and b) to find a function that relates U.S. Dollars to Canadian Dollars.

Now compose the two functions. You are starting with dollars, going to Euros, and then going to Canadian dollars. Working from the inside out, how should the functions be composed?

2. You make a purchase at a local store, but what you've bought is too big to take home in your car. For a small fee, you arrange to have the store deliver your purchase. You pay for your purchase, plus the sales tax, plus the fee. The tax rate is 8.5% and the delivery fee is $30.
a. Write a function P(x) for the total, including taxes, on the purchase amount x.

If the purchase amount is $100, how much are the taxes? What is the total cost? If the purchase amount is $200, how much are the taxes? What is the total cost? If the purchase amount is $x, how much are the taxes? What is the total cost?

b. Write a function T(x) for the total, including the delivery fee, on the purchase amount x.

If the purchase is $100, what is the delivery fee? What is the total? If the purchase is $200, what is the delivery fee? What is the total? If the purchase is $x, what is the delivery fee? What is the total?

c. Calculate and interpret (P*T)(x) and (T*P)(x). Which results in a lower cost to you?

The "*" character means "multiplied by" or "times". Is that what you mean, or does this exercise ask you to compare the compositions? Thanks!

[smbroadb]

I didn't mean multiply I just didn't know how to put the circle in between I wanted to compare the composite functions

[theshadow]

I didn't mean multiply I just didn't know how to put the circle in between I wanted to compare the composite functions

You can use the letter "o" for this when the context is composition. Just use spacing so "f composed w/ g" is "f o g" not the word "fog".