Question

I have $1.10 worth of coins in my pocket. The only types of coins are nickles and dimes. If there are 16 coins how many of each coin are there

Answer 1

this is a system of equations

only nickels and dimes

n + d = 16
.05n + .10d = 1.10

can you solve this?

Answer 2

I like doing coin problems in cents, but otherwise do it exactly as @johnweldon1993 has done here:

n + d = 16
5n + 10d = 110

The advantage to using cents instead of dollars is that you don't have to deal with decimals — but you should get the same answer either way.

Answer 3

yeah @whpalmer4 I was thinking about doing it without decimals...more fun this way though! more chances to make mistakes so better to concentrate :D lol

Answer 4

you with us @fridayman ?

Answer 5

it's funny, in other pursuits, I'm a big fan of doing things the less comfortable way, so that when forced to do it the less comfortable way, it isn't so unfamiliar or difficult. In math, however, I seem not to do that :-)

Answer 6

Yes, so once you get

n + d = 10
.05n + .10d = 1.10

Is it just basically a substitution problem from there?

Answer 7

I know some kids who do these problems like this:

you've got 16 coins. Let them all be nickels. Then you would have 16 * 5 cents = 80 cents. That's not enough, so let's exchange some of those nickels for dimes. Each one you change bumps the total value up by 10-5 = 5 cents. 80 cents was $1.10 - 80 cents = 30 cents too low. 30 cents / 5 cents per exchange = 6 coins to exchange. That means 10 nickels and 6 dimes...

Answer 8

Basically yes...so since you seem to know what to do....just let us know what you get for an answer

Answer 9

@whpalmer4 O.o oh no! haha that's too much XD perhaps I wouldn't go THAT complicated! haha

Answer 10

My grandmother kept the books for the family business, and used to accumulate huge amounts of change, so we did problems like this all the time when I was a little kid :-)

Answer 11

@whpalmer4 See...that's an awesome way to get started into math! haha kudos to your grandmother!

Answer 12

any kid gets interested in arithmetic when there's money involved :-)

Answer 13

this is true! haha...actually it's funny how many kids I tutor...when I change it into a money problem or a "friends" problem...they'll get it like *snap* that lol...but then put it in mathematical terms and the looks would be O.o haha

Answer 14

I cant get it

Answer 15

well lets see what you are doing...post what steps you were doing...

Answer 16

0.5(n + d = 10)
0.5n + .10d = 1.10

0.5n + 0.5d = 5
0.5n + .10d = 1.10

Answer 17

I get -0.5d = 3.9

Answer 18

n + d = 16 ---> n = 16 - d
now sub 10 - d in for n in the other equation
.05n + .10d = 1.10
.05(16 - d) + .10d = 1.10
.80 - .05d + 10d = 1.10
.05d = 1.10 - .80
.05d = .30
d = .30/.05
d = 6
now sub 6 in for d
n + d = 16
n + 6 = 16
n = 16 - 6
n = 10
check....
.05n + .10d = 1.10
.05(10) + .10(6) = 1.10
.50 + .60 = 1.10
1.10 = 1.10 (correct)
ANSWER : There are 10 nickels totaling 50 cents and 6 dimes totaling 60 cents. All together, there are 16 coins totaling 1.10.
Any questions ?

Answer 19

@fridayman where were you getting 0.5 from? a nickel is $0.05, or 5 cents.

@texaschic101 showed you substitution, I'll show you elimination:

\[n+d = 16\]\[5n+10d = 110\]
Multiply first equation by -5:
\[-5n-5d=-80\]\[5n+10d=110\]------------------ adding
\[0n + 5d = 3\]\[5d=30\]\[
d=6\]\[n+d=16\]\[n+6=16\]\[n=10\]
checking:
\[5(10) + 10(6) = 50+60 = 110\checkmark\]