Problem 11 · 2023 Math Kangaroo
Hard
Fractions, Decimals & Percents
percent-multiplier
Jennifer wants to save water. She reduces the water pressure and thus reduces the water usage by one quarter. Furthermore, she reduces the time she takes a shower by one quarter. By which fraction in total does she reduce the water usage for her shower?
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Answer: E — by \(\frac{7}{16}\)
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Hint 1 of 2
Water used = pressure × time; cutting each by a quarter multiplies each factor by 3/4.
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Hint 2 of 2
Multiply the two reduction factors and compare with the original.
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Approach: multiply the two scaling factors
- Reducing by a quarter leaves 3/4 of the pressure and 3/4 of the time.
- New usage = (3/4)(3/4) = 9/16 of the original.
- The reduction is 1 − 9/16 = 7/16.
- So she saves 7/16 of the water.
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