I am threading blue and purple beads onto a necklace in the ratio $$2 : 5$$. I use $$98$$ beads in total. How many more purple beads than blue do I use? 
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The ratio $$2 : 5$$ means that $$2$$ in $$7$$ beads are blue and $$5$$ in $$7$$ purple. Since $$98 \div 7 = 14$$, there are $$28$$ blue and $$70$$ purple beads, hence $$70 - 28 = 42$$ more purple than blue. 