Maria has $5.05 in quarters and dimes. The number of quarters exceeds twice the number of dimes by 1. Find the number she has of each kind.

Let's solve the problem step-by-step:

Step 1: Let's assume the number of dimes Maria has is "x".
Step 2: The number of quarters is then "2x + 1" (given that the number of quarters exceeds twice the number of dimes by 1).
Step 3: The value of dimes is calculated by multiplying the number of dimes by 10 cents: 10x.
Step 4: The value of quarters is calculated by multiplying the number of quarters by 25 cents: 25(2x + 1).
Step 5: The value of dimes and quarters together is given as $5.05: 10x + 25(2x + 1).
Step 6: Simplifying the equation: 10x + 50x + 25 = 505.
Step 7: Combining like terms: 60x + 25 = 505.
Step 8: Subtracting 25 from both sides: 60x = 480.
Step 9: Dividing both sides by 60: x = 8.

Therefore, Maria has 8 dimes and twice as many quarters, which is 2(8) + 1 = 17 quarters.

To find the number of quarters and dimes Maria has, we can set up a system of equations based on the information given.

Let's assume the number of dimes is "x". Therefore, the number of quarters is twice that number plus one, so it would be 2x + 1.

Now, let's calculate the total value of the coins Maria has. The value of one quarter is $0.25, so we multiply the number of quarters (2x + 1) by $0.25. The value of one dime is $0.10, so we multiply the number of dimes (x) by $0.10.

The total value of the coins is given as $5.05, so we can set up the equation:

0.25(2x + 1) + 0.10x = 5.05

Now, we can solve for x:

0.50x + 0.25 + 0.10x = 5.05
0.60x + 0.25 = 5.05
0.60x = 4.80
x = 8

Therefore, Maria has 8 dimes. Now, we can find the number of quarters by substituting this value back into the expression 2x + 1:

2(8) + 1 = 16 + 1 = 17

So, Maria has 17 quarters and 8 dimes.

q = 2d+1

10d+25q = 505
10d + 25(2d+1) = 505
10d + 50d + 25 = 505
60d = 480
d = 8
q = 17

80 + 425 = 505