To determine the amount of money based on the number of dimes (d) and quarters (q), we can use the following steps:

Conversion rates:

• Each dime is worth 10 cents.
• Each quarter is worth 25 cents.

Formula to calculate total value:

• Total in cents = $10 \times d + 25 \times q$
• Total in dollars = $\frac{10 \times d + 25 \times q}{100}$

Now, let's express the values for both dollars and cents:

a) Total in dollars:

$\text{Total in dollars} = \frac{10d + 25q}{100}$

b) Total in cents:

$\text{Total in cents} = 10d + 25q$

For example:

• If you have 5 dimes (d = 5) and 3 quarters (q = 3):
  • Total in cents = $10 \times 5 + 25 \times 3 = 50 + 75 = 125$ cents.
  • Total in dollars = $\frac{125}{100} = 1.25$ dollars.

Would you like to use specific values for dimes and quarters, or would you like further details on the calculations?

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Relative questions:

1. How many quarters and dimes make exactly 2 dollars?
2. What if we added nickels and pennies to the mix?
3. How would the formula change for different currencies, like euros?
4. How can you quickly convert a dollar amount into a coin combination?
5. What is the least number of coins to make 75 cents?

Tip:

Always remember to double-check your units when switching between cents and dollars!