2019 AMC 10B Problems/Problem 11

Revision as of 16:00, 14 February 2019 by Mathisdecent (talk | contribs) (Solution)

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?

$\textbf{(A) } 5\qquad\textbf{(B) } 10 \qquad\textbf{(C) }25  \qquad\textbf{(D) } 45  \qquad \textbf{(E) } 50$

Solution

Call the amount of marbles in each jar x, because they are equivalent. Thus, x/10 is the amount of green marbles in 1, and x/9 is the amount of green marbles in 2. x/9+x/10=19x/90, 19x/90=95, and x=450 marbles in each jar. Because the 9/10 is the amount of blue marbles in jar 1, and 8/9 is the amount of blue marbles in jar 2, 9x/10-8x/9=x/90, so there must be 5 more marbles in jar 1 than jar 2. The answer is A

See Also

2019 AMC 10B (ProblemsAnswer KeyResources)
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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