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There were 156 more silver balloons than gold balloons at a party. After 5/6 of the silver balloons and 3/4 of the gold balloons burst, there were 106 balloons left. How many balloons were there altogether at first?

 Feb 5, 2022
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We start by assigning the variable \(s\) to the silver balloons and \(g\) to the gold balloons. The first thing they said was that \(g + 156 = s\). The second was that \((s-\frac{5s}{6})+ (g - \frac{3g}{4}) = \frac{s}{6} + \frac{g}{4} = 106\). Subsituting the first equation into the second gives us \(\frac{g+156}{6} + \frac{g}{4} = 106\)

=> \(\frac{g}{6} + \frac{156}{6} + \frac{g}{4} = \frac{g}{6} + \frac{g}{4} + 26 = 106\)

=> \(\frac{g}{6} + \frac{g}{4} = 80\)

=> \(2g + 3g = 5g = 80 * 12 = 960\)

=> \(g = \frac{960}{5} = 192\)

and having g = 192 in the first equation gives us \(s = 192 + 156 = 348\) so the total number of balloons in the start is \(348 + 192 = 540\).

 

(Please upvote!)

 Feb 5, 2022

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