please help me with this really hard word problem?
Suppose a bag contains at total of 5280 quarters; some of which are Canadian and some of which are US. The Canadian dollar is worth 87 US cents. An ounce of gold is worth US$ 989.
a) If the number of US coins the bag contains is N, write an algebraic expression for how many US dollars they are worth. [Hint: how much is one quarter worth? Two quarters? N quarters?]
b) Write an expression for how many ounces of gold the US coins will buy. [Hint: how do you determine how much of something you can get for a given amount of money based on its price?]
c) Write an expression in terms of N (the number of US coins) for the number of Canadian coins in the bag. [Hint: the whole is the sum of the parts. What number is given as the whole?]
d) Give an expression (in terms of N, the number of US coins) for how many US dollars the Canadian coins are worth. [Hint: how many Canadian dollars are the Canadian coins worth and how much in US dollars is a Canadian dol. worth
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Wow, that is certainly quite the word problem, lol.
One thing you should know is the word problems are asking for expressions. That means you make up an algebra formula, but you don’t have to solve it.
Now to give a crack at it…
a) Okay, one US quarter is equal to… a quarter of a dollar, or .25 of a dollar. If you have two US quarters, it’s equal to (.25) * 2, or .50 of a dollar (half). What you’re doing is, you take the number of quarters you have and multiply it by .25… so, if they say you have N quarters, the amount of dollars it is worth is .25 * N, or .25N is your answer here.
b) Now you have to figure out how many ounces of gold the US quarters can buy. The problem tells you an ounce of gold is $989. But, this depends on how many US quarters you actually have. The problem told you to make N the number of quarters you have, so we’ll stick with that here. You need to figure out how many dollars you have, but we did that in part A, so .25N is how many dollars you have. To figure out how many ounces of gold you can get, you have to divide .25N by 989… each time you get 989 dollars out of the quarters, you can get one ounce. So it ends up being (.25N) / 989.
c)Now you need to figure out how many Canadian coins are there. The problem tells you that you have 5280 quarters. You also know that you have N US quarters, whatever the actual number may be. In this case, whatever is not a US quarter, is a Canadian quarter, so you take the total amount of quarters (5280) and subtract all of the US quarters (N) and you have the amount of Canadian quarters. Or, the answer is 5280 - N.
d)Now, you need to figure out how many US dollars the Canadian coins are worth. Geez, lol. The amount of Canadian coins you have is 5280 - N (we figured it out for part c). If you multiply that by 4, you have a Canadian dollar, so that’s 4(5280 - N). But, a Canadian dollar is only .87 of a US dollar. So… you need to multiply a Canadian dollar by .87 to get a US dollar. That ends up being .87 * 4 * (5280 - N)… or to make it look nicer, .87 * 4 = 3.48, so 3.48(5280 - N) is the final answer. Whew!