a. List three different combinations of coins, each with a value of 30% of a dollar. b. List two different combinations of coins, each with a value of 140% of a dollar. 3. For each... a. List three different combinations of coins, each with a value of 30% of a dollar. b. List two different combinations of coins, each with a value of 140% of a dollar. 3. For each coin, state its worth as a percentage of $1. 4. Complete the double number line to show percentages of $50.

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Understand the Problem

The question is asking to solve problems related to percentages, including combinations of coins worth specific percentages of a dollar and completing a number line with specific dollar amounts and corresponding percentages. It requires calculating and possibly understanding value representation in terms of money.

Answer

Combinations for 30%: 1 quarter + 1 nickel, 3 dimes, 30 pennies. Combinations for 140%: 1 dollar + 1 quarter + 1 dime + 1 nickel, 7 dimes + 3 quarters. Percentages of $50 on the double number line are: 0 (0%), 12.50 (25%), 50 (100%), 62.50 (125%).
Answer for screen readers
  • Combinations for 30% of a dollar:

    1. 1 quarter + 1 nickel
    2. 3 dimes
    3. 30 pennies
  • Combinations for 140% of a dollar:

    1. 1 dollar + 1 quarter + 1 dime + 1 nickel
    2. 7 dimes + 3 quarters
  • The completed double number line for percentages of $50:

    • 0 (0%)
    • 12.50 (25%)
    • 50 (100%)
    • 62.50 (125%)

Steps to Solve

  1. Finding 30% of a Dollar

To find the value that is 30% of a dollar, we can calculate it using the formula:

$$ \text{Value} = \text{Percentage} \times \text{Total} = 0.30 \times 1 = 0.30 \text{ dollars} $$

This means we need to create combinations of coins that sum to $0.30.

  1. Listing Combinations for 30% of a Dollar

Here are three combinations of coins that add up to $0.30:

  • Combination 1: 1 quarter (25 cents) + 1 nickel (5 cents)
  • Combination 2: 3 dimes (30 cents)
  • Combination 3: 30 pennies (30 cents)
  1. Finding 140% of a Dollar

Next, to find the value that is 140% of a dollar:

$$ \text{Value} = 1.40 \text{ dollars} $$

This means we need combinations of coins that sum to $1.40.

  1. Listing Combinations for 140% of a Dollar

Here are two combinations of coins that add up to $1.40:

  • Combination 1: 1 dollar coin + 1 quarter (25 cents) + 1 dime (10 cents) + 1 nickel (5 cents)
  • Combination 2: 7 dimes (70 cents) + 3 quarters (75 cents)
  1. Completing the Dollar Amounts for Percentages of $50

To complete the double number line, calculate the percentages and corresponding dollar amounts:

  • $12.50 is 25% of $50: $$ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 = \frac{12.50}{50} \times 100 = 25% $$

  • $50 is 100% of $50: $$ \text{Percentage} = \frac{50}{50} \times 100 = 100% $$

  • $62.50 is 125% of $50: $$ \text{Percentage} = \frac{62.50}{50} \times 100 = 125% $$

  • Combinations for 30% of a dollar:

    1. 1 quarter + 1 nickel
    2. 3 dimes
    3. 30 pennies
  • Combinations for 140% of a dollar:

    1. 1 dollar + 1 quarter + 1 dime + 1 nickel
    2. 7 dimes + 3 quarters
  • The completed double number line for percentages of $50:

    • 0 (0%)
    • 12.50 (25%)
    • 50 (100%)
    • 62.50 (125%)

More Information

  • 30% of a dollar is equivalent to 30 cents, which can be represented by various combinations of U.S. coins.
  • 140% of a dollar shows how much more than one dollar the amount is, in this case, $1.40.
  • The double number line is a useful way to visualize percentages against the actual dollar amounts, helping to understand the relationship between them.

Tips

  • Mixing up percentages and their corresponding dollar values; always cross-check calculations.
  • Not realizing that there can be multiple combinations of coins for the same amount; brainstorming different combinations can be helpful.

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