If 60\% of a number x is 40, then what is x\% of 60?

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{"type":"doc","content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1:","type":"text"},{"text":" Find ","type":"text"},{"attrs":{"latex":"x"},"type":"math_inline"},{"text":" from ","type":"text"},{"attrs":{"latex":"60\%"},"type":"math_inline"},{"text":" of ","type":"text"},{"type":"math_inline","attrs":{"latex":"x = 40"}},{"text":".","type":"text"}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"\frac{60}{100} \cdot x = 40 \implies x = \frac{40 \times 100}{60} = \frac{200}{3}"}},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2:","type":"text"},{"text":" Compute ","type":"text"},{"attrs":{"latex":"x\%"},"type":"math_inline"},{"text":" of ","type":"text"},{"attrs":{"latex":"60"},"type":"math_inline"},{"text":":","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"\frac{x}{100} \cdot 60 = \frac{60x}{100} = \frac{60}{100} \cdot x = 40"},"type":"math_block"},{"content":[{"text":"Key Insight:","type":"text","marks":[{"type":"bold"}]},{"text":" Notice that ","type":"text"},{"type":"math_inline","attrs":{"latex":"x\%"}},{"text":" of ","type":"text"},{"attrs":{"latex":"60 = \frac{x \cdot 60}{100} = \frac{60 \cdot x}{100} = 60\%"},"type":"math_inline"},{"text":" of ","type":"text"},{"attrs":{"latex":"x = 40"},"type":"math_inline"},{"text":". The percentage operation is commutative: ","type":"text"},{"attrs":{"latex":"a\%"},"type":"math_inline"},{"text":" of ","type":"text"},{"type":"math_inline","attrs":{"latex":"b = b\%"}},{"text":" of ","type":"text"},{"attrs":{"latex":"a"},"type":"math_inline"},{"text":".","type":"text"}],"type":"paragraph"}]}

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