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A particular dishwasher uses $4$ gallons of water per load. Their advertising claims that hand washing the dishes uses $6$ times as much water. According to this estimate, how many gallons of water would it save to wash $215$ loads using the dishwasher instead of by hand

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Estimate population size using proportions

Full solution

Q. A particular dishwasher uses

4

gallons of water per load. Their advertising claims that hand washing the dishes uses

6

times as much water. According to this estimate, how many gallons of water would it save to wash

215

loads using the dishwasher instead of by hand

Calculate water per load: Calculate the amount of water used per load when washing by hand. $\newline$ Hand washing uses $6$ times as much water as the dishwasher. $\newline$ $6 \times 4$ gallons per load = $24$ gallons per load.
Total water for $215$ loads by hand: Calculate the total amount of water used for $215$ loads when washing by hand. $\newline$ $215$ loads $\times 24$ gallons per load $= 5160$ gallons.
Total water for $215$ loads by dishwasher: Calculate the total amount of water used for $215$ loads using the dishwasher. $\newline$ $215$ loads $\times 4$ gallons per load $= 860$ gallons.
Calculate water saved: Calculate the amount of water saved by using the dishwasher for $215$ loads instead of washing by hand. $\newline$ Water saved $=$ Water used by hand $-$ Water used by dishwasher. $\newline$ Water saved $= 5160$ gallons $- 860$ gallons $= 4300$ gallons.

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