+54 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?
+17 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!)
