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The expression 100+20m100 + 20m gives the volume of water, in liters, in Marcel's pool after Marcel spends mm minutes filling his pool. What is the volume of water, in liters, in Marcel's pool after he fills it for 5145 \frac{1}{4} minutes?

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Full solution

Q. The expression 100+20m100 + 20m gives the volume of water, in liters, in Marcel's pool after Marcel spends mm minutes filling his pool. What is the volume of water, in liters, in Marcel's pool after he fills it for 5145 \frac{1}{4} minutes?
  1. Identify Given Expression: Identify the given expression and the value of mm. The expression for the volume of water in Marcel's pool is 100+20m100 + 20m, where mm is the number of minutes spent filling the pool. We are given that Marcel fills the pool for 5145 \frac{1}{4} minutes.
  2. Convert to Improper Fraction: Convert the mixed number 5145 \frac{1}{4} minutes into an improper fraction to make the calculation easier.\newline5145 \frac{1}{4} minutes can be written as (5×4+1)/4=(20+1)/4=214(5 \times 4 + 1)/4 = (20 + 1)/4 = \frac{21}{4} minutes.
  3. Substitute Value and Calculate: Substitute the value of mm into the expression to find the volume of water after 5145 \frac{1}{4} minutes.\newlineUsing m=214m = \frac{21}{4}, the expression becomes:\newlineVolume = 100+20×(214)100 + 20 \times \left(\frac{21}{4}\right)
  4. Perform Multiplication: Perform the multiplication within the expression.\newlineVolume = 100+20×(214)=100+(20×214)100 + 20 \times \left(\frac{21}{4}\right) = 100 + \left(\frac{20 \times 21}{4}\right)
  5. Calculate Product and Divide: Calculate the product of 2020 and 2121, then divide by 44.\newlineVolume =100+4204= 100 + \frac{420}{4}
  6. Add to Find Total Volume: Divide 420420 by 44.\newlineVolume = 100+105100 + 105
  7. Add to Find Total Volume: Divide 420420 by 44.\newlineVolume = 100+105100 + 105 Add 100100 to 105105 to find the total volume.\newlineVolume = 205205 liters

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