Final answer:
To solve this problem, we can set up a system of equations. Let's assume the number of dimes is x. Since the pepper carrier has six more quarters than dimes, the number of quarters would be x + 6. And since the pepper carrier has three times as many nickels as quarters, the number of nickels would be 3(x + 6). The total value of the coins can be expressed as: 0.1x (dimes) + 0.25(x + 6) (quarters) + 0.05(3(x + 6)) (nickels) = 6.90.
Step-by-step explanation:
To solve this problem, we can set up a system of equations.
Let's assume the number of dimes is x.
Since the pepper carrier has six more quarters than dimes, the number of quarters would be x + 6.
And since the pepper carrier has three times as many nickels as quarters, the number of nickels would be 3(x + 6).
The total value of the coins can be expressed as: 0.1x (dimes) + 0.25(x + 6) (quarters) + 0.05(3(x + 6)) (nickels) = 6.90.
Simplifying the equation, we get: 0.1x + 0.25x + 1.5 + 0.15x + 0.9 = 6.90.
Combining like terms, we have: 0.5x + 2.4 = 6.90.
Subtracting 2.4 from both sides, we get: 0.5x = 4.50.
Dividing both sides by 0.5, we get: x = 9.
Therefore, the pepper carrier has 9 dimes, 9 + 6 = 15 quarters, and 3(15) = 45 nickels.