Question 19754: ms. lynch has 21 coins in nickle and dimes.Their total value is $1.65.How many of each coin does she have
Found 2 solutions by Paul, mmm4444bot:
Answer by Paul(988)   (Show Source):
You can put this solution on YOUR website! Let nickets represent x
Let dimes represent y
x+y=21
y=21-x (equation 1)
dimes=10 (x100)
nickels=5 (x100)
sum=165 (x100)
5(x)+10(y)=165 (Sub in equation 1)
5x+10(21-x)=165
5x+210-10x=165
-5x=-45
x=9
21-9= 12
Therefore, there are 9 nickels and 12 dimes
Answer by mmm4444bot(95) (Show Source):
You can put this solution on YOUR website! Hello There:
Start by assigning variable names for the two unknown amounts that we are asked to find.
x = number of nickels
y = number of dimes
Each nickel is worth $0.05 and each dime is worth $0.10, so we can write an equation because we're told that their total is $1.65.
0.05*x + 0.10*y = 1.65
(The asterisks mean multiplication.)
We're also told that:
x + y = 21
If you don't like working with the decimal numbers in the first equation, then multiply both sides by 100 to get whole numbers.
5*x + 10*y = 165
x + y = 21
This is a system of two equations with two variables. Off the top of my head, I can think of at least five different ways to solve this system. You didn't ask any questions or tell us what method to use, so I'll just guess.
I'm going to show you the "substitution" method. The strategy is to solve one of the equations for x, and then substitute the resulting expression for x in the other equation. This results in an equation with only one variable (for which we can solve easily).
I'll solve the second equation for x by subtracting y from both sides:
x = 21 - y
Now that we know 21 - y is the same as x, we substitute it for x in the first equation:
5*x + 10*y = 165
5*(21 - y) + 10*y = 165
105 - 5*y + 10*y = 165
5*y = 60
y = 12
Now that we know the value of y, we can find the value of x from our equation above:
x = 21 - y
x = 21 - 12
x = 9
Ms. Lynch has 9 nickels and 12 dimes. Let's check our result.
Is 9 + 12 equal to 21 coins? Yes, it is.
9 nickels is $0.45, and 12 dimes is $1.20. Do these amounts add up to $1.65? Yes, they do. Our answer is correct.
~ Mark
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