Jack has a collection of new nickels and quarters. He has a total of 50 coins worth $10.30. How many of each coin does he have?
Let's assume Jack has x nickels and y quarters.
1. The total number of coins Jack has is given as 50:
x + y = 50 -- equation (1)
2. The total value of the coins is given as $10.30:
0.05x + 0.25y = 10.30 -- equation (2)
To solve these equations, we can use the substitution method or the elimination method. Let's use the elimination method:
Multiply equation (1) by 0.05:
0.05x + 0.05y = 2.50 -- equation (3)
Now subtract equation (3) from equation (2) to eliminate the x variable:
0.05x + 0.25y - 0.05x - 0.05y = 10.30 - 2.50
This simplifies to:
0.20y = 7.80
Divide both sides by 0.20 to isolate y:
y = 7.80 / 0.20
Calculating this:
y = 39
Substitute the value of y back into equation (1):
x + 39 = 50
Subtract 39 from both sides to calculate x:
x = 50 - 39
Calculating this:
x = 11
Therefore, Jack has 11 nickels and 39 quarters.
To find out how many nickels and quarters Jack has, we can set up a system of equations based on the given information.
Let's assume Jack has x nickels and y quarters.
The value of x nickels is 5x cents, and the value of y quarters is 25y cents.
According to the problem, Jack has a total of 50 coins. Therefore, the equation representing the total number of coins is:
x + y = 50
The total value of the coins is $10.30, which is equivalent to 1030 cents. We can write the equation for the total value as:
5x + 25y = 1030
Now we have a system of two equations:
x + y = 50 ...(1)
5x + 25y = 1030 ...(2)
To solve the system of equations, we can use the method of substitution or elimination.
First, let's solve equation (1) for x:
x = 50 - y
Now substitute this value of x in equation (2):
5(50 - y) + 25y = 1030
Simplify the equation:
250 - 5y + 25y = 1030
20y = 780
y = 39
Now substitute the value of y into equation (1):
x + 39 = 50
x = 50 - 39
x = 11
Therefore, Jack has 11 nickels and 39 quarters.
n+q = 50
5n+25q = 1030
Now just solve for n and q.