Question 897265: Okay, so I have a word problem that I need some help with I've already tried a few things and I just don't understand how to write it as an equation so that I can solve it:
PIGGY BANKS: When a child emptied her coin bank, she had a collection of pennies, nickels, and dimes. There were a total of 20 pennies and a combine total of 25 nickels and dimes. if the coins had a total value of 220 cents, how many nickels and dime were in the bank?
so I have:
20 pennies; 25 nickels and dimes = $ .220
N = nickels
D = dimes
VALUE: nickel = 5 cent; dime = 10 cents; penny = 1 cent
---- number * value = total value
---- 20+5N+10D=220?.... did I write that write, because I don't think I did. I need help writing the right equation so if you could please get back to me.
Found 2 solutions by MathTherapy, KMST:
Answer by MathTherapy(10557)   (Show Source):
You can put this solution on YOUR website!
Okay, so I have a word problem that I need some help with I've already tried a few things and I just don't understand how to write it as an equation so that I can solve it:
PIGGY BANKS: When a child emptied her coin bank, she had a collection of pennies, nickels, and dimes. There were a total of 20 pennies and a combine total of 25 nickels and dimes. if the coins had a total value of 220 cents, how many nickels and dime were in the bank?
so I have:
20 pennies; 25 nickels and dimes = $ .220
N = nickels
D = dimes
VALUE: nickel = 5 cent; dime = 10 cents; penny = 1 cent
---- number * value = total value
---- 20+5N+10D=220?.... did I write that write, because I don't think I did. I need help writing the right equation so if you could please get back to me.
Let the number of nickels and dimes be N, and D, respectively
Since there are a total of 25 nickels and dimes, then we can say that: N + D = 25 ------- eq (i)
We already know that from the 220 cents, or $2.20, pennies make up 20 cents, or $0.20, so the value
of the 25 nickels and dimes is 200 cents, or $2
Therefore, value equation is: .05N + .1D = 2 ------ eq (ii)
If decimals are a problem, then you can multiply equation (ii) by 20 to get: N + 2D = 40 ------ eq (ii)
The 2 equations, thus formed are:
N + D = 25 ------ eq (i)
N + 2D = 40 ----- eq (ii)
- D = - 15 ------ Subtracting eq (ii) from eq (i)
D, or number of dimes =  , or 
N + 15 = 25 ------ Substituting 15 for D in eq (i)
N, or number of nickels = 25 - 15, or 
You can do the check!!
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Answer by KMST(5328)  (Show Source):
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