Marcus saved 20 coins consisting of 25 and 1 coins. How many of each kind does he have is the coins amount to 10.25?
To find the number of each kind of coin Marcus has, we can set up a system of equations based on the given information.
Let's say the number of 25-cent coins Marcus has is "x", and the number of 1-cent coins he has is "y".
The total value of the 25-cent coins is 25x cents, and the total value of the 1-cent coins is 1y cents.
We know that the total number of coins is 20, so we have our first equation:
x + y = 20
We also know that the total value of the coins is $10.25, which is equal to 1025 cents. So our second equation is:
25x + 1y = 1025
Now we have a system of equations:
x + y = 20
25x + 1y = 1025
We can solve this system of equations to find the values of x and y.
First, it is convenient to multiply the first equation by 25 to match the coefficient of x in the second equation:
25(x + y) = 25(20)
25x + 25y = 500
Now we can eliminate y by subtracting the second equation from this new equation:
(25x + 25y) - (25x + 1y) = 500 - 1025
24y = -525
Finally, we can solve for y:
y = -525 / 24
y ≈ -21.875
But since the number of coins cannot be negative, we know that y must be a whole number, so we can round it up to the nearest whole number:
y = 22
Now we can substitute this value back into the first equation to solve for x:
x + 22 = 20
x = 20 - 22
x = -2
Again, we can't have a negative number of coins, so this solution is not valid.
This means that there is no valid solution for the number of 25-cent and 1-cent coins that Marcus has if the total value of the coins is $10.25.