Maths Olympiad Prep

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Algebra Difficulty 2.1 Junior Find the answer

Suppose that 23\tfrac{2}{3} of 1010 bananas are worth as much as 88 oranges. How many oranges are worth as much as 12\tfrac{1}{2} of 55 bananas?

Pick one

Solution

If 23⋅10 bananas=8 oranges\frac{2}{3}\cdot10\ \text{bananas}=8\ \text{oranges}, then 12⋅5 bananas=(12⋅5 bananas)⋅(8 oranges23⋅10 bananas)=3 oranges⟹(C)\frac{1}{2}\cdot5\ \text{bananas}=\left(\frac{1}{2}\cdot 5\ \text{bananas}\right)\cdot\left(\frac{8\ \text{oranges}}{\frac{2}{3}\cdot10\ \text{bananas}}\right)=3\ \text{oranges}\Longrightarrow\mathrm{(C)}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.