SOLUTION: a jar contains n nickels and d dimes. there are 20 coins in the jar, and the total value of the coins is $1.40. how many nickels and dimes are in the jar? (hint:Nickels are $0.05 a

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Question 717333: a jar contains n nickels and d dimes. there are 20 coins in the jar, and the total value of the coins is $1.40. how many nickels and dimes are in the jar? (hint:Nickels are $0.05 and dimes are worth $0.10.)
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
This problem can be done with the money amounts expressed in terms of dollars or expressed in terms of cents. I like working with cents because it eliminates the decimals. So I am going to use 140 cents instead of $1.40, 5 instead of $0.05 and 10 instead of $0.10.

To solve for two variables we will need two equations. One equation will reflect the number of coins and the other will reflect the values of these coins. For the number of coins we have the fact that there are 20 coins:
n + d = 20
For the values of the coins we have to figure out that if each nickel is worth 5 cents then n nickels will be worth 5n cents. Similarly, d dimes will be worth 10d cents. We're told that the total value is 140 cents. So our equation is:
5n + 10d = 140

So our system is:
n + d = 20
5n + 10d = 140
There are quite a few methods that are taught for solving systems like this. Usually the Substitution and Linear Combination methods are taught first. (Several others come later.) I'm going to choose the Linear Combination method because you're likely to have seen it before and because I've found that many students prefer this method.

The first part of Linear Combination is to line up opposite terms. If I multiply the first equation by -5 I can get the n terms of the two equations to be opposites of each other. (Or I could multiply by -10 and make the d terms opposites.) Multiplying the first equation by -5 we get:
-5n + (-5d) = -100
5n + 10d = 140
Now we add the equations. The n terms cancel.
5d = 40
Divide by 5:
d = 8

Now we can use this value for d and one of the original equations to find the value for n:
n + (8) = 20
Subtracting 8:
n = 12

So there are 12 nickels and 8 dimes.