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Count collections of coins

A collection of pennies, nickels, dimes, and quarters is understood as a total value in cents, found by combining each coin’s fixed value rather than counting the coins themselves; the total can also be represented in dollars and cents using decimal notation. The reasoning includes grouping by denomination and connecting equivalent totals, without extending to complex coin systems, large monetary amounts, or formal change-making strategies.

Detailed Explanation: Count collections of coins

Each kind of coin has a fixed value:

  • Penny: 11 cent
  • Nickel: 55 cents
  • Dime: 1010 cents
  • Quarter: 2525 cents

To find the total value, multiply the number of each coin by its value, then add.

Example: Find the value of 33 pennies, 22 nickels, 11 dime, and 22 quarters.

  1. Find the value of each group:

    • 33 pennies: 3×1=33 \times 1 = 3 cents
    • 22 nickels: 2×5=102 \times 5 = 10 cents
    • 11 dime: 1×10=101 \times 10 = 10 cents
    • 22 quarters: 2×25=502 \times 25 = 50 cents

  2. Add the group values:

3+10+10+50=73 cents3 + 10 + 10 + 50 = 73\text{ cents}

  1. Write the total as dollars and cents. Since 100100 cents equals 11 dollar, 7373 cents is:

$0.73\$0.73

So, the collection is worth 7373 cents, or 0.73$.

Learn by doing: Count collections of coins

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    Coin Math - Count Total - Dimes and Quarters

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