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The expression 100+20 m gives the volume of water, in liters, in Marcel's pool after Marcel spends m minutes filling his pool. What is the volume of water, in liters, in Marcel's pool after he fills it for 5(1)/(4) minutes?

The expression 100+20m 100+20 m gives the volume of water, in liters, in Marcel's pool after Marcel spends m m minutes filling his pool. What is the volume of water, in liters, in Marcel's pool after he fills it for 514 5 \frac{1}{4} minutes?

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Q. The expression 100+20m 100+20 m gives the volume of water, in liters, in Marcel's pool after Marcel spends m m minutes filling his pool. What is the volume of water, in liters, in Marcel's pool after he fills it for 514 5 \frac{1}{4} minutes?
  1. Understand the expression: Understand the expression and what is asked.\newlineThe expression given is 100+20m100 + 20m, where mm represents the minutes spent filling the pool. We need to find the volume of water in the pool after Marcel fills it for 5145\frac{1}{4} minutes.
  2. Convert to improper fraction: Convert the mixed number to an improper fraction.\newline514minutes\frac{5\frac{1}{4}}{\text{minutes}} is a mixed number. To work with it easily, we convert it to an improper fraction. 514minutes=(5×4+1)4=(20+1)4=214\frac{5\frac{1}{4}}{\text{minutes}} = \frac{(5 \times 4 + 1)}{4} = \frac{(20 + 1)}{4} = \frac{21}{4} minutes.
  3. Substitute value of m: Substitute the value of m into the expression.\newlineNow we substitute m=214m = \frac{21}{4} into the expression 100+20m100 + 20m to find the volume of water in the pool.\newlineVolume = 100+20×(214)100 + 20 \times \left(\frac{21}{4}\right)
  4. Perform multiplication: Perform the multiplication.\newlineNow we multiply 2020 by 214\frac{21}{4}.\newline20×(214)=(20×21)4=420420 \times \left(\frac{21}{4}\right) = \frac{(20 \times 21)}{4} = \frac{420}{4}
  5. Perform division: Perform the division.\newlineNow we divide 420420 by 44.\newline420/4=105420 / 4 = 105
  6. Add initial volume: Add the initial volume to the volume added.\newlineNow we add the volume from the multiplication to the initial volume of 100100 liters.\newlineVolume = 100+105=205100 + 105 = 205 liters

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