SOLUTION: How do I translate to a system of equations and solve? A collection of nickels and dimes is worth $16.05. There are 218 coins in all. How many are nickels and how many are dim

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Question 135052This question is from textbook Algebra 1 workbook
: How do I translate to a system of equations and solve?
A collection of nickels and dimes is worth $16.05. There are 218 coins in all. How many are nickels and how many are dimes?
This question is from textbook Algebra 1 workbook

Answer by vleith(2517) About Me  (Show Source):
You can put this solution on YOUR website!
Let d be the number of dimes.
Let n be the number of nickels.
Given:
total number of coins = 218 = number of dimes + number of nickels =>
218+=+d%2Bn
total value of coins = 16.05 = 0.10d + 0.05n (multiply the value of each coin by the number and then add the totla for both types of coins) -->
1605+=+10d+%2B+5n lets convert from dollars to pennies to make things easier (we just multiplied the eqaution above by 10)
You now have 2 equations and 2 unknowns, so you can solve this.
218+=+d%2Bn
218+-+n+=+d
1605+=10d+%2B+5n
1605+=+10%28218+-+n%29+%2B+5n
1605+=+2180+-+10n+%2B+5n
-575+=+-5n
115+=+n
You have 115 nickles.
218-115 = 103 dimes
Check your answer
10.30 in dimes + 5.75 in nickels = $16.05. check!