During a long-distance relay event, Emek and Luna organized hydration stations along the course. The race guide recommended 30 liters of water for every 20 runners. When registration increased to 35 runners at one station, they set up a proportion to calculate the new amount of water needed. They repeated the process for other stations with different numbers of runners and checked that each calculation matched the planned supply ratio. Thanks to their careful planning, every hydration station remained properly stocked, and the race finished without any runners running out of water.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Keep liters and runners in the same order in both ratios.
The race guide recommends 30 liters of water for every 20 runners. Which proportion correctly models the amount of water, x liters, needed for 35 runners?
30/20 = x/3530/35 = x/2020/30 = x/3535/30 = x/20Correct! The proportion compares liters per runner consistently.
Write the ratio as liters to runners in both fractions.
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Hint
Compare 40 runners with 20 runners, then scale the water by the same factor.
Using the recommended ratio of 30 liters for every 20 runners, how many liters of water are needed for 40 runners?
Correct! Doubling the runners doubles the amount of water.
Use the same scale factor for both runners and liters.
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Hint
Find the amount of water for 35 runners using a proportion before checking the claim.
A volunteer says that 45 liters of water is enough for 35 runners because it follows the same ratio as 30 liters for 20 runners. Is the volunteer correct?
Yes, because 45 is 15 liters more than 30.No, because 35 runners need 52.5 liters to keep the same ratio.Yes, because 45 ÷ 35 = 30 ÷ 20.No, because 35 runners need exactly 50 liters.Correct! The proportion gives 52.5 liters, so 45 liters is not enough.
Calculate the proportional amount first, then compare it with 45 liters.
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