Let's break down problem step by: ### Step 1 Find the relationship between scales and B - On A: Ice point =400. Steam = 440 A = 40 A units- On scale: point = . B Steam point =180. Difference = 60. B units So, **1 unit on scale A = (60/40) = 1.5 units on scale B**. **Explanation:** The difference between the steam and ice points on each scale allows us to find how many B units correspond to one A unit. --- ### Step 2: Convert the given temperature from scale A to scale B - Given: Temperature = 25.° above ice point on scale A So, A reading = 400. + 25. = 425. A Now, convert 425. A to scale B: - Fraction of the way from ice to steam point on A: \[ \text{Fraction} = \frac{425. - 400.}{40.} = \frac{25.}{40.} = .625 \] - Corresponding B value: \[ \text{B value} = 120. + .625 \times 60. = 120. + 37.5 = 157.5 B \] **Explanation:** We convert the temperature to a fraction of the interval between the fixed points and apply that fraction to the interval on scale B. --- ## **Final Answer** - **(a) 9 A = 13.5 B** - **(b) 25.° above ice point on A = 157.5 B**

# Temperature Conversion Between Scales A and B To convert the temperatures between scales A and B, we will follow two main steps. ## Step 1: Determine the Relationship Between Scales A and B 1. **Identify Fixed Points:** - Ice point on scale A: 400 A - Steam point on scale A: 440 A - Ice point on scale B: 120 B - Steam point on scale B: 180 B 2. **Calculate Differences:** - Difference in scale A: \[ 440 A - 400 A = 40 A \] - Difference in scale B: \[ 180 B - 120 B = 60 B \] 3. **Find Conversion Factor:** - The relationship can be expressed as: \[ 1 \text{ unit on scale A} = \frac{60 B}{40 A} = 1.5 B \] **Explanation:** This conversion factor indicates that for every unit increase on scale A, there is a corresponding increase of 1.5 units on scale B. --- ## Step 2: Convert the Given Temperature from Scale A to Scale B 1. **Given Temperature:** - Temperature = 25° above ice point on scale A. - Therefore, actual temperature on scale A: \[ 400 A + 25 A = 425 A \] 2. **Calculate Fraction of the Interval on Scale A:** - Fraction from ice to steam point: \[ \text{Fraction} = \frac{425 A - 400 A}{40 A} = \frac{25 A}{40 A} = 0.625 \] 3. **Convert to Scale B:** - Corresponding B value: \[ \text{B value} = 120 B + (0.625 \times 60 B) = 120 B + 37.5 B = 157.5 B \] **Explanation:** This step involves determining how far along the temperature on scale A is from its ice point, and then applying that same fraction to the range of scale B to find the corresponding temperature. --- ## Final Answer - **(a)** For 9 A: \[ 9 A \times 1.5 = 13.5 B \] - **(b)** For 25° above ice point on A: \[ 25° A \text{ corresponds to } 157.5 B \]