Answer:
2 : 9
Explanation:
Put the given numbers in the expression and simplify:
bikes before : total bikes
= (bikes before) : (bikes before) + (bikes bought)
= 6 : (6 +21)
= 6 : 27
= 2 : 9
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Additional comment
A question like this would do little to convince you ratios have some usefulness. There appears to be no point whatever to knowing the fraction of older bikes.
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Ratios are used many places in the real world. Perhaps the ratios you encounter most frequently are tax rates.
If you spend any time cooking, you know that certain ratios of ingredients produce better taste and/or texture than other ratios, and you know that (generally) changing the quantity a recipe produces will involve changing all the ingredient amounts by the same ratio.
Finance, health, time, diet budgets are often specifies as ratios: 14% APR, 2.3 infant deaths per 1000 live births, 2 hours outside class for each hour in class, 25% of calories from fat, and so on.
Of course, chemistry is all about ratios. CO₂ and H₂O are perhaps some of the more important ratios in the world right now. These specific ratios of carbon, hydrogen, and oxygen atoms make substances that are both life-giving and life-threatening. Much study is directed at determining and maintaining appropriate ratios of these substances relative to others.