SOLUTION: solve and show the equations used for the solution Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?

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Question 121934: solve and show the equations used for the solution
Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You have two relationships in a coin problem. One relates the number of coins and the other concerns the value of the coins.

Let n be the number of nickels, and d be the number of dimes. So we know that n%2Bd=50.

Since nickels are worth 5 cents each, the value of the nickels in this problem is 5n cents. Similarly, the value of the dimes is 10d cents. Just to keep everything conveniently in terms of integers, let's convert $3.50 to 350 cents. Now we can say:

5n%2B10d=350

Solve the first equation for n: n=50-d, and substitute this expression for n into the second equation.

cartoon%285%2Ared%28n%29%2B10d=350%2C5%2Ared%28%2850-d%29%29%2B10d=350%29

Now distribute the 5 and collect terms:

cartoon%28red%285%2A%2850-d%29%29%2B10d=350%2Cred%28250-5d%29%2B10d=350%29
cartoon%28250+-red%285d%2B10d%29=350%2C250%2Bred%285d%29=350%29
cartoon%28red%28250%29%2B5d=red%28350%29%2C5d=red%28350-250%29%2C5d=red%28100%29%29
cartoon%285d=red%28100%29%2Cd=red%2820%29%29

So there are 20 dimes, and there are 50-20=30 nickels.

Check: 30 nickels are worth $1.50, 20 dimes are worth $2.00. $1.50 plus $2.00 are $3.50. Answer checks.