Tiffanny has 100 coins in dimes and nickels. She has a total of $5.80. How many of each coin does she have. Write the equations then solve.
10d + 5(100-d) = 580
10d + 500 - 5d = 580
5d = 80
d = 16
so, 16 dimes: $1.60
84 nickels: $4.20
I'm doing systems of equations so can you do it
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X+y= 100. Y=-x+100
10x+5y=580. Y=-2x+116
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that Tiffany has "x" dimes and "y" nickels.
The value of a dime is 10 cents, so the value of "x" dimes is 10x cents.
Similarly, the value of a nickel is 5 cents, so the value of "y" nickels is 5y cents.
According to the problem, Tiffany has 100 coins in total. Therefore, we can write the first equation as:
x + y = 100 (Equation 1)
Additionally, we are given that the total value of the coins is $5.80, which is equivalent to 580 cents. Therefore, we can write the second equation as:
10x + 5y = 580 (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (x and y). We can solve this system of equations using various methods, such as substitution, elimination, or graphical methods.
Since the first equation is already solved for "x" or "y," we can use substitution to solve this system of equations.
From Equation 1, we have:
x = 100 - y
Substituting this value of "x" into Equation 2, we get:
10(100 - y) + 5y = 580
We can now simplify and solve this equation to find the value of "y." Once we have the value of "y," we can substitute it back into Equation 1 to find the value of "x."
So, using the steps explained, we get:
1000 - 10y + 5y = 580
-5y = 580 - 1000
-5y = -420
y = (-420) / (-5)
y = 84
Now that we have the value of "y" as 84, we can substitute it back into Equation 1 to find the value of "x."
x + 84 = 100
x = 100 - 84
x = 16
Therefore, Tiffany has 16 dimes and 84 nickels.