Julie has 8 more than three times as many quarters as dimes. The total value of the coins is $12.20. How many of each kind of coin does she have?
To solve this problem, we can set up two equations based on the given information.
Let's assume that Julie has 'x' dimes and 'y' quarters.
According to the problem, Julie has 8 more than three times as many quarters as dimes. This can be written as:
y = 3x + 8 ----(Equation 1)
The total value of the coins is $12.20. We know that a dime is worth $0.10 and a quarter is worth $0.25. So, we can write another equation for the total value:
0.10x + 0.25y = 12.20 ----(Equation 2)
Now that we have our equations, we can solve them to find the values of 'x' and 'y'.
First, let's solve Equation 1 for 'y':
y = 3x + 8
Next, substitute this value of 'y' into Equation 2:
0.10x + 0.25(3x + 8) = 12.20
Simplify the equation:
0.10x + 0.75x + 2 = 12.20
0.85x + 2 = 12.20
0.85x = 10.20
x = 12
Now we can substitute the value of 'x' back into Equation 1 to find 'y':
y = 3(12) + 8
y = 36 + 8
y = 44
Therefore, Julie has 12 dimes and 44 quarters.
d = 3q+8
.10d + .25q = 12.20
.10(3q+8) + .25q = 12.20
Solve for q, then d.