2019 AMC 10B Problems/Problem 1
- The following problem is from both the 2019 AMC 10B #1 and 2019 AMC 12B #1, so both problems redirect to this page.
Contents
Problem
Alicia had two containers. The first was full of water and the second was empty. She poured all the water from the first container into the second container, at which point the second container was full of water. What is the ratio of the volume of the first container to the volume of the second container?
Solution
Let the first jar's volume be and the second's be . It is given that . We find that
We already know that this is the ratio of smaller to larger volume because it is less than
Solution 2
We can set up a ratio to solve this problem. If x is the volume of the first container, and y is the volume of the second container, then:
Cross Multiplying allows us to get . Thus the ratio of the volume of the first container to the second container is
An alternate solution is to plug in some maximum volume for the first container - let's say , so there was a volume of 60 in the first container, and then the second container also has a volume of , so you get . Thus, .
See Also
2019 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
2019 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by First Problem |
Followed by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
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