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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?

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  1. AriPotta
    • 3 years ago
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    5n + 10d = 330 n + d = 42

  2. liza2
    • 3 years ago
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    n is the number of nickels and d is the number of dimes.

  3. AriPotta
    • 3 years ago
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    so you gotta use the second equation to solve for d

  4. AriPotta
    • 3 years ago
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    or n, but i would do d

  5. AriPotta
    • 3 years ago
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    so what does d equal?

  6. El_Pollo
    • 3 years ago
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    D=576

  7. AriPotta
    • 3 years ago
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    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
    • 3 years ago
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    and then you can substitute 42 - n for d in the first equation

  9. AriPotta
    • 3 years ago
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    so 5n + 10d = 330 would be 5n + 10(42 - n) = 330. is this making sense?

  10. El_Pollo
    • 3 years ago
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    Yes, but we have to have a system of equations

  11. AriPotta
    • 3 years ago
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    the first thing i posted was our system of equations

  12. AriPotta
    • 3 years ago
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    now we're solving it

  13. El_Pollo
    • 3 years ago
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    Oh right sorry

  14. AriPotta
    • 3 years ago
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    so do you know what to do from there? from 5n + 10(42 - n) = 330?

  15. El_Pollo
    • 3 years ago
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    ok

  16. El_Pollo
    • 3 years ago
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    so just distribute and then solve from there?

  17. AriPotta
    • 3 years ago
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    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
    • 3 years ago
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    i get a negative

  19. AriPotta
    • 3 years ago
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    |dw:1349754629184:dw|

  20. AriPotta
    • 3 years ago
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    does that make sense?

  21. El_Pollo
    • 3 years ago
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    yes i see were i made my mistake i forgot the negative sign

  22. AriPotta
    • 3 years ago
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    so now we know that 18 + d = 42 and we can solve for d

  23. El_Pollo
    • 3 years ago
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    right plug in 18 in the n part

  24. AriPotta
    • 3 years ago
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    yup, so how many dimes are there?

  25. El_Pollo
    • 3 years ago
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    there's 24

  26. AriPotta
    • 3 years ago
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    yep :) 24 dimes and 18 nickels

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