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Algebra Difficulty 3.7 AMC 10/12 Find the answer South Africa

Water freezes at 0∘0^\circ Celsius and boils at 100∘100^\circ Celsius. On the SAMO scale, water freezes at 20∘20^\circ and boils at 170∘170^\circ. The two scales are linearly related. What is the temperature on the SAMO scale if it is 80∘80^\circ on the Celsius scale?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

A temperature of 80∘80^\circ C is 80%80\% of the distance from freezing point to boiling point, so on the SAMO scale the reading is
20+80100(170−20)=20+120=140∘. 20 + \frac{80}{100}(170 - 20) = 20 + 120 = 140^\circ.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.