Question

A few countries such as the USA officially use Fahrenheit as a unit for measuring temperature. Other countries prefer Celsius over Fahrenheit. The two different scales are related by the linear equation `(F - 32)/9 = C/5`. A scientist wants to store an experimental solution between a temperature range of 68°F and 77°F.

Based on the above information, answer the following questions:

1. The algebraic representation of the given information in degree Celsius is:

(a) `68 < 5/9 C + 32 ≤ 77, C ∈ R`

(b) `68 ≤ 5/9 C - 32 ≤ 77, C ∈ R`

(c) `68 < 9/5 C - 32 < 77, C ∈ R`

(d) `68 < 9/5 C + 32 < 77, C ∈ R`

2. The solution set for the temperature in degree Celsius is:

(a) {C ∈ R : 18 C < 23}

(b) {C ∈ R : 20 C < 25}

(c) {C ∈ R : 22 C < 27}

(d) {C ∈ R : 25 C < 30}

3. What is the range of the temperature in degree Celsius?

(a) between 20°C and 25°C 

(b) between 25°C and 30°C

(c) between 18°C and 23°С

(d) between 22°C and 27°C

4. Which of the following is the graphical representation of the temperature in degree Celsius?

(a)

(b)

(c)

(d)

5. If the minimum temperature that can be maintained in a particular refrigerator is 0°C, what is the possible temperature range of the refrigerator on a Fahrenheit scale?

(a) `F > 160/9`

(b) `F < 160/9`

(c) F > 32

(d) F < 32

Answer 1

1. Given,

⇒ `(F - 32)/9 = C/5`

⇒ `F - 32 = 9/5 C`

⇒ `F = 9/5 C + 32`

Given,

A scientist wants to store an experimental solution between a temperature range of 68°F and 77°F.

∴ `68 < 9/5 C + 32 < 77`

Hence, Option (d) is the correct option.

2. Solving,

⇒ `68 < 9/5 C + 32 < 77`

Solving L.H.S of inequation,

⇒ `68 < 9/5 C + 32`

⇒ `9/5 C + 32 > 68`

⇒ `9/5 C > 68 - 32`

⇒ `9/5 C > 36`

⇒ 9C > 36 × 5

⇒ 9C > 180

⇒ `C > 180/9`

⇒ C > 20   ...(1)

Solving R.H.S of inequation,

⇒ `9/5 C + 32 < 77`

⇒ `9/5 C < 77 - 32`

⇒ `9/5 C < 45`

⇒ 9C < 45 × 5

⇒ 9C < 225

⇒ `C < 225/9`

⇒ C < 25   ...(2)

From (1) and (2) we get,

∴ 20 < C < 25

Since C ∈ R

Solution set = {C ∈ R : 20 < C < 25}

Hence, Option (b) is the correct option.

3. The solution set for the temperature in degree Celsius is: {C ∈ R : 20 < C < 25}

Hence, Option (a) is the correct option.

4. Solution set = {C ∈ R : 20 < C < 25}

Hence, Option (a) is the correct option.

5. Given,

Minimum temperature that can be maintained = 0°C

⇒ `F = 9/5 C + 32`

Minimum temperature that can be maintained in term of Fahrenheit scale:

⇒ `F = 9/5 xx (0) + 32`

⇒ F > 32

Hence, Option (c) is the correct option.