Tristan has $3.75 in quarters and dimes. She has 21 coins. How many of each coin does she have?
quarters ---- x
dimes ------ 21-x
25x + 10(21-x) = 375
25x + 210 - 10x = 375
15x = 165
x = 11
Tristan has 11 quarters and 10 dimes
To find out how many quarters and dimes Tristan has, we can set up a system of equations based on the given information.
Let's assume Tristan has x quarters and y dimes.
The value of x quarters is 25x cents.
The value of y dimes is 10y cents.
According to the problem, Tristan has a total of 21 coins, so we can write the first equation:
x + y = 21 Equation 1
The total value of the quarters and dimes combined is $3.75, which is equivalent to 375 cents. We can write the second equation:
25x + 10y = 375 Equation 2
Now, we have a system of equations consisting of Equation 1 and Equation 2. We can solve this system to find the values of x (number of quarters) and y (number of dimes).
First, we solve Equation 1 for x in terms of y:
x = 21 - y
Now, substitute this value of x into Equation 2:
25(21 - y) + 10y = 375
Distribute the 25:
525 - 25y + 10y = 375
Combine like terms:
-15y = 375 - 525
-15y = -150
Divide both sides by -15:
y = (-150) / (-15)
y = 10
Now that we know the number of dimes (y = 10), we can substitute this value back into Equation 1 to solve for x:
x + 10 = 21
x = 21 - 10
x = 11
So, Tristan has 11 quarters and 10 dimes.