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Answer to Q6

If 32° Fahrenheit equals 0° Celsius and 212° Fahrenheit equals 100° Celsius. At what temperature will Fahrenheit and Celsius be the same?

If,
32°F = 0°C [eqn i]
212°F = 100°C [eqn ii]

When will x°F = x°C [eqn iii]

From eqns i, ii, and iii above, we can say

(212 - 32) ÷ (212 - x) = (100 - 0) ÷ (100 - x)

180 ÷ (212 - x) = 100 ÷ (100 - x) [eqn iv]

Cross multiplying eqn iv
100(212 - x) = 180(100 - x)

21,200 - 100x = 18,000 - 180x [eqn v]

Collecting like terms of eqn v

-100x + 180x = 18,000 - 21,200

80x = -3,200 [eqn vi]

Dividing eqn vi through by 80

x = -3,200 ÷ 80 = -40

Answer: -40



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Answer to Q6

If 32° Fahrenheit equals 0° Celsius and 212° Fahrenheit equals 100° Celsius. At what temperature will Fahrenheit and Celsius be the same?

If,
32°F = 0°C [eqn i]
212°F = 100°C [eqn ii]

When will x°F = x°C [eqn iii]

From eqns i, ii, and iii above, we can say

(212 - 32) ÷ (212 - x) = (100 - 0) ÷ (100 - x)

180 ÷ (212 - x) = 100 ÷ (100 - x) [eqn iv]

Cross multiplying eqn iv
100(212 - x) = 180(100 - x)

21,200 - 100x = 18,000 - 180x [eqn v]

Collecting like terms of eqn v

-100x + 180x = 18,000 - 21,200

80x = -3,200 [eqn vi]

Dividing eqn vi through by 80

x = -3,200 ÷ 80 = -40

Answer: -40

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