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South African Mathematics Olympiad Second Round

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

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

Your answer

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

Solution

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

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