## El_Pollo 3 years ago 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?

1. AriPotta

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

2. liza2

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

3. AriPotta

so you gotta use the second equation to solve for d

4. AriPotta

or n, but i would do d

5. AriPotta

so what does d equal?

6. El_Pollo

D=576

7. 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

8. AriPotta

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

9. AriPotta

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

10. El_Pollo

Yes, but we have to have a system of equations

11. AriPotta

the first thing i posted was our system of equations

12. AriPotta

now we're solving it

13. El_Pollo

Oh right sorry

14. AriPotta

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

15. El_Pollo

ok

16. El_Pollo

so just distribute and then solve from there?

17. 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

18. El_Pollo

i get a negative

19. AriPotta

|dw:1349754629184:dw|

20. AriPotta

does that make sense?

21. El_Pollo

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

22. AriPotta

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

23. El_Pollo

right plug in 18 in the n part

24. AriPotta

yup, so how many dimes are there?

25. El_Pollo

there's 24

26. AriPotta

yep :) 24 dimes and 18 nickels