Difference between revisions of "2019 AMC 10B Problems/Problem 11"
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− | Call the amount of marbles in each jar <math>x</math>, because they are equivalent. Thus, <math>x/10</math> is the amount of green marbles in <math>1</math>, and <math>x/9</math> is the amount of green marbles in <math>2</math>. <math>x | + | Call the amount of marbles in each jar <math>x</math>, because they are equivalent. Thus, <math>x/10</math> is the amount of green marbles in <math>1</math>, and <math>x/9</math> is the amount of green marbles in <math>2</math>. <math>\frac{x}{9}+\frac{x}{10}=\frac{19x}{90}</math>, <math>\frac{19x}{90}=95</math>, and <math>x=450</math> marbles in each jar. Because the <math>\frac{9x}{10}</math> is the amount of blue marbles in jar <math>1</math>, and <math>\frac{8x}{9}</math> is the amount of blue marbles in jar <math>2</math>, <math>\frac{9x}{10}-\frac{8x}{9}=\frac{x}{90}</math>, so there must be <math>5</math> more marbles in jar <math>1</math> than jar <math>2</math>. The answer is <math>(\boxed{A})</math> |
(Edited by Lcz) | (Edited by Lcz) |
Revision as of 23:45, 14 February 2019
Problem
Two jars each contain the same number of marbles, and every marble is either blue or green. In Jar 1 the ratio of blue to green marbles is 9:1, and the ratio of blue to green marbles in Jar 2 is 8:1. There are 95 green marbles in all. How many more blue marbles are in Jar 1 than in Jar 2?
Solution
Call the amount of marbles in each jar , because they are equivalent. Thus, is the amount of green marbles in , and is the amount of green marbles in . , , and marbles in each jar. Because the is the amount of blue marbles in jar , and is the amount of blue marbles in jar , , so there must be more marbles in jar than jar . The answer is
(Edited by Lcz)
See Also
2019 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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 |
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