2005 PMWC Problems/Problem I14
Problem
On a balance scale, three green balls balance six blue balls, two yellow balls balance five blue balls and six blue balls balance four white balls. How many blue balls are needed to balance four green, two yellow and two white balls?
Solution
From the given, we have the equations
![\[3g = 6b \Longrightarrow g = 2b\]](http://latex.artofproblemsolving.com/5/f/6/5f60887b227441d3862d1ee98b0432c25813ec90.png)
![\[2y = 5b \Longrightarrow y = \frac{5}{2}b\]](http://latex.artofproblemsolving.com/2/d/5/2d55865cdf8b228c22e55ade16923f969057740e.png)
![\[4w = 6b \Longrightarrow w = \frac{3}{2}b\]](http://latex.artofproblemsolving.com/4/a/f/4af0d778d88d87a3a12b1c1fb704cc0c78650992.png)
Substuting gives us 
, and our answer is 16.
See also
| 2005 PMWC (Problems) | ||
| Preceded by Problem I13 |
Followed by Problem I15 | |
| I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
