A girl had 20 coins in nickels and dimes whose Sun was $1.40. She spent 65¢ using 8 coins. She has __ nickels.
5n+10(8-n) = 65
-5n = -15
n = 3
she spent 3 nickels and 5 dimes.
So, starting with N nickels and D dimes,
5N+10(20-N) = 140
-5N = -60
N=12
So, she is left with 9 nickels.
To find out how many nickels the girl has, we can use the information given.
We are told that the girl has a total of 20 coins in nickels and dimes. Let's assume she has "x" nickels and "y" dimes.
Since she has a total of 20 coins, we can write the equation: x + y = 20.
We are also given that the sum of the coins she has is $1.40. Each nickel is worth 5 cents and each dime is worth 10 cents, so the value equation can be written as: 5x + 10y = 140.
Now, we know that she spent 65¢ using 8 coins, but we don't know the breakdown of nickels and dimes for these 8 coins. We also don't know if any of the coins she spent were nickels. Therefore, we cannot use this information to directly determine the number of nickels she has.
To solve these equations, we can use a method called substitution or elimination. Let's use the substitution method to find the value of "x" (the number of nickels).
First, we can rearrange the first equation to solve for "y": y = 20 - x.
Now, substitute this expression for "y" in the value equation: 5x + 10(20 - x) = 140.
Simplifying this equation gives: 5x + 200 - 10x = 140.
Combining like terms gives: -5x + 200 = 140.
To isolate "x" (the number of nickels), we can subtract 200 from both sides: -5x = -60.
Dividing both sides by -5 gives: x = 12.
Therefore, the girl has 12 nickels.
Note: The given information about the girl spending 65¢ using 8 coins was not used to directly determine the number of nickels.