2023 AMC 10B Problems/Problem 1
Problem
Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely but runs out of juice when the fourth glass is only 
full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into the fourth glass so that all four glasses will have the same amount of juice?
Solution 1
We let 
denote how much juice we take from each of the first 
children and give to the 
th child.
We can write the following equation: 
, since each value represents how much juice each child (equally) has in the end. (Each of the first three children now have 
juice, and hte fourth child has 
more juice on top of their initial 
.)
Solving, we see that 
~Technodoggo
Solution 2
We begin by assigning a variable 
to the capacity of one full glass. Quickly we see the four glasses are equivalent to 
. In order for all four glasses to have the same amount of orange juice, they have to each have 
. This means each full glass must contribute 
where 
. 
~vsinghminhas
Vide Solution 1 by SpreadTheMathLove
https://www.youtube.com/watch?v=SUnhwbA5_So
See also
| 2023 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
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| All AMC 10 Problems and Solutions | ||
| 2023 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 | |
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