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Samantha has a coin collection. She keeps 2 of the coins in her box, which is 25% of the collection. How many total coins are in her collection? Answer:

Samantha has a coin collection. She keeps 22 of the coins in her box, which is 25% 25 \% of the collection. How many total coins are in her collection?\newlineAnswer:

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Full solution

Q. Samantha has a coin collection. She keeps 22 of the coins in her box, which is 25% 25 \% of the collection. How many total coins are in her collection?\newlineAnswer:
  1. Understand Relationship: Understand the relationship between the part and the whole in percentage problems.\newlineSamantha has 22 coins, which represent 25%25\% of her total collection. We need to find the total number of coins in her collection.
  2. Set Up Equation: Set up the equation based on the percentage formula: Percent (as a decimal) ×\times Whole = Part.\newlineHere, the part is 22 coins, and the percent is 25%25\% (or 0.250.25 as a decimal). Let the total number of coins be represented by 'xx'.\newlineThe equation is: 0.25×x=20.25 \times x = 2.
  3. Solve for 'x': Solve for 'x' by isolating it on one side of the equation.\newlineDivide both sides of the equation by 0.250.25 to find the value of 'x'.\newlinex=20.25x = \frac{2}{0.25}.
  4. Perform Division: Perform the division to find the total number of coins. x=20.25=8x = \frac{2}{0.25} = 8.
  5. Verify Solution: Verify the solution by checking if 25%25\% of the total number of coins equals 22. 25%25\% of 88 is (25100)×8=2(\frac{25}{100}) \times 8 = 2.

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