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

\[3g = 6b \Longrightarrow g = 2b\] \[2y = 5b \Longrightarrow y = \frac{5}{2}b\] \[4w = 6b \Longrightarrow w = \frac{3}{2}b\]

Substuting gives us $4g + 2y + 2w = 4(2b) + 2\left(\frac{5}{2}b\right) + 2\left(\frac{3}{2}b\right) = 16b$, 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
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