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NCERT Class XI Mathematics - Linear Inequalities - Solutions

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Question : 62 of 65
Marks: +1, -0
A solution is to be kept between 68°F and 77°F. What is the range in temperature in degree celcius (C) if the celsius/Fahrenheit (F) conversion formula is given by F = 95\frac{9}{5} C + 32 ?
Solution:  
We have, F = 95\frac{9}{5} C + 32
but, 68 < F < 77
∴ 68 < 95\frac{9}{5} C + 32 < 77
Subtracting 32 from each side, we get
- 32 < 95\frac{9}{5} C + 77 - 32 ⇒ 36 < 95\frac{9}{5} C < 45
Multiplying each side by 5/9, we get 36 × 59\frac{5}{9} < C < 45 × 59\frac{5}{9}
⇒ 20 < C < 25
∴ Required temperature is between 20°C and 25°C.
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