Before the regional tournament, Tara, Emek, and Luna prepared practice stations for their team. They noticed that each station needed a balanced mix of equipment. One station had 12 balls, 4 cones, and 8 training markers. They wrote the relationships as ratios: 12:4:8. By comparing the ratios between stations, they adjusted the supplies so each area had the same equipment balance. With the correct proportions in place, the team practiced smoothly and was ready for the tournament.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Divide each part of the ratio by the same greatest common factor.
The equipment balance at one station is 12:4:8 for balls, cones, and training markers. What is the simplified ratio?
3:1:26:2:412:2:84:1:3Correct! Dividing 12:4:8 by 4 gives the simplified ratio 3:1:2.
Check that all parts of the ratio are divided by the same number.
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Hint
Use the simplified ratio to find how many balls match each cone.
A second practice station keeps the same equipment balance as 12:4:8. If it has 15 cones, how many balls should it have?
Correct! The ratio has 3 balls for every 1 cone, so 15 cones need 45 balls.
Use the relationship between balls and cones in the simplified ratio.
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Hint
Simplify both ratios and compare their relationships.
Tara compares two stations. Station A has 12 balls, 4 cones, and 8 markers. Station B has 18 balls, 6 cones, and 12 markers. What can she conclude?
Station A has a greater equipment balance than Station B.Station B has twice as many cones as Station A.Both stations have the same equipment ratio.Station B has a different ratio because it has more equipment.Correct! Both stations simplify to the same ratio, 3:1:2.
Having more items does not always mean having a different ratio.
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