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# How much

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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 $$348 + 192 = 540$$.

Feb 5, 2022