A Bank teller has $16.50 in quarters and dimes. There are 25 fewer quarters than dimes. How many quarters does he have?
number of dimes --- x
number of quarters -- x-25
10x + 25(x-25) = 1650
10x + 25x - 625 = 1650
35x = 2275
x = 65
So 65 dimes and 40 quarters.
check:
65 dimes = $6.50
40 quarters = $10
total = 16.50
Let's assume the number of dimes the bank teller has is D.
We know that the value of a quarter is $0.25, and the value of a dime is $0.10.
The total value of the quarters would be 0.25 * (D - 25), since the bank teller has 25 fewer quarters than dimes.
Similarly, the total value of the dimes would be 0.10 * D.
Given that the total value of quarters and dimes is $16.50, we can set up the equation:
0.25 * (D - 25) + 0.10 * D = 16.50
Simplifying this equation, we get:
0.25D - 6.25 + 0.10D = 16.50
0.35D - 6.25 = 16.50
0.35D = 22.75
D = 22.75 / 0.35
D ≈ 65
Therefore, the bank teller has approximately 65 dimes.
Since there are 25 fewer quarters than dimes, the number of quarters would be:
65 - 25 = 40
Therefore, the bank teller has 40 quarters.
To solve this problem, we can break it down into steps:
Step 1: Let's assume the number of dimes the bank teller has is 'x'.
Step 2: We know that there are 25 fewer quarters than dimes, so the number of quarters is 'x - 25'.
Step 3: The value of each quarter is $0.25, and the value of each dime is $0.10.
Step 4: The total value of the quarters can be calculated by multiplying the number of quarters by its value: 0.25 * (x - 25).
Step 5: The total value of the dimes can be found by multiplying the number of dimes by its value: 0.10 * x.
Step 6: The sum of the values of the quarters and dimes is equal to $16.50, so we can set up the equation: 0.25 * (x - 25) + 0.10 * x = 16.50.
Step 7: Simplify the equation: 0.25x - 6.25 + 0.10x = 16.50.
Step 8: Combine like terms: 0.35x - 6.25 = 16.50.
Step 9: Add 6.25 to both sides of the equation: 0.35x = 22.75.
Step 10: Divide both sides of the equation by 0.35 to solve for x: x = 65.
Therefore, the bank teller has 65 dimes.
To find the number of quarters, substitute the value of 'x' into the equation 'x - 25'.
So, the bank teller has 65 - 25 = 40 quarters.