Math Help

So I'm doing this word problem with Sam. I have the answer but I don't
know WHY it is the answer. Can any of you out there in cyberspace
help?

Here is the question:
Sarim has $1 in coins. One-fifth of the coins are dimes,
two-fifteenths are nickels, and two-thirds are pennies. Tell how many
of each coin he has.

The answer:
6 dimes; 4 nickels; 20 pennies; making 30 coins

Now that makes sense because all the fractions work into the total
number of coins nicely. (i.e. 1/5 of 30 is 6... pennies) But how would
I have attacked this problem and more importantly (to me) why would I
do it that way...

Anyone?

over 2 years ago (Facebook) responded:

What are you looking for? The NUMBER OF COINS. Let that be X. X is always what you're looking for. ;)

Now set up the equation based on what you know.
-- sum of coins is $1
-- ratio of specific type of coins to total coins

I do a lot of this in my head, so here's how do you find the equation?
$ value of dimes + $ value of nickels + $ value of pennies = $1 (given)
$ value of dimes = # of dimes * $0.10 (common knowledge; not stated in the text)
# of dimes = 1/5X (given)
... or ...
$ value of dimes = 1/5X * $0.10
... or ...

********************************
1/5X * $0.1 + 2/15X * $0.05 + 2/3X * $0.01 = $1
********************************

BTW, you'll also want to cross-check that
1/5 + 2/15 + 2/3 = 1
to ensure that you've accounted for all the coins.

Since you have one variable and one equation, solve for X. Two variables will need two equations, i.e. you need one unique equation for each variable.

If you use a calculator, you might get a fraction from rounding errors (like 29.999999). Or you can find the common denominator (15) elaborated below.

3/15X * $0.1 + 2/15X * $0.05 + 10/15X * $0.01 = $1
Factor out the 15
3X * $0.1 + 2X * $0.05 + 10X * $0.01 = $15
Factor out the dollar ($) to make it look easier.
3X * 0.1 + 2X * 0.05 + 10X * 0.01 = 15

You should also do a dimensional analysis to ensure everything is in the same units. You don't want want
$ + $ + tomatoes = $
in the SAME equation; that just doesn't work.

In this case, you have
1/5X * $0.1
number * X * $, so the first will be a $ unit.
2/15X * $0.05
number * X * $, so the second will be a $ unit.
10/15X * $0.01
number * X * $, so the third will be a $ unit.
finally the other side, $1, is in $ also, so we have $ + $ + $ = $, all the dimensions are the same so we should be good.

Solve for X by simplifying ONE STEP AT A TIME!.

I'd multiply everything by 100 to get rid of the cents.
3X * 10 + 2X * 5 + 10X * 1 = 1500
30X + 10X + 10X = 1500
50X = 1500
5X = 150
X = 30

Now plug 30 in for X to ensure that you didn't screw up the math.
1/5(30) * $0.1 + 2/15(30) * $0.05 + 2/3(30) * $0.01 = $1
(6) * $0.1 + (4) * $0.05 + (20) * $0.01 = $1
$0.60 + $0.20 + $0.20 = $1

Since that checks, you can be confident in your answer.

Why do it this way? You're using the information given. I can't think of any other way to do it. The trick is to convert words into numbers. In this case, each sentence is an equation.

If you have more questions, please ask.

Wilhelm vF

1. Establish your equations.
2. Check you dimensions (units).
-- dimensional analysis (ensure units are correct; e.g ft + ft = ft; inch + inch = inch, etc.)
3. Use additional information to quicly check that your equation(s) are correct before you solve the equation(s).
4. Solve the equation(s) one step at a time.
5. Plug your answer back into your equation(s) to ensure it works.

The Sinister Scribe

The Sinister Scribe

Math Help