Solve using a system of equations:
There is a collection of nickels and dimes worth $3.30. There are 42 coins in all. How many are there of each kind?

- anonymous

- katieb

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- AriPotta

5n + 10d = 330
n + d = 42

- anonymous

n is the number of nickels and d is the number of dimes.

- AriPotta

so you gotta use the second equation to solve for d

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## More answers

- AriPotta

or n, but i would do d

- AriPotta

so what does d equal?

- anonymous

D=576

- AriPotta

no, what you gotta do it find out what d is compared to n.
so it's n + d = 42. what you do with that is subtract n from both sides to get d = 42 - n

- AriPotta

and then you can substitute 42 - n for d in the first equation

- AriPotta

so 5n + 10d = 330 would be 5n + 10(42 - n) = 330.
is this making sense?

- anonymous

Yes, but we have to have a system of equations

- AriPotta

the first thing i posted was our system of equations

- AriPotta

now we're solving it

- anonymous

Oh right sorry

- AriPotta

so do you know what to do from there? from 5n + 10(42 - n) = 330?

- anonymous

ok

- anonymous

so just distribute and then solve from there?

- AriPotta

yea, distribute the 10 into the parentheses and then solve for n and once you know how many nickels there are, just substitute that for n in the second equation and solve for d

- anonymous

i get a negative

- AriPotta

|dw:1349754629184:dw|

- AriPotta

does that make sense?

- anonymous

yes i see were i made my mistake i forgot the negative sign

- AriPotta

so now we know that 18 + d = 42 and we can solve for d

- anonymous

right plug in 18 in the n part

- AriPotta

yup, so how many dimes are there?

- anonymous

there's 24

- AriPotta

yep :) 24 dimes and 18 nickels

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