Abra Land and Bogo Land use two different scales, viz. Scale-A and Scale-B respectively to measure temperature. These two scales are related linearly. Measurements on the Scale-A of 10 and 20 correspond to the measurements on the Scale-B of 37 and 54 respectively. The corresponding measurement of the temperature on Scale-B for a measurement of 100 on Scale-A will be _____________ .

To solve the problem, we need to determine the relationship between Scale-A and Scale-B using the given points and then use this relationship to find the corresponding temperature on Scale-B for a temperature of 100 on Scale-A.

### Step 1: Establish the linear relationship between Scale-A and Scale-B
Given:
- Scale-A: \( A_1 = 10 \), \( A_2 = 20 \)
- Scale-B: \( B_1 = 37 \), \( B_2 = 54 \)

Assume the relationship between Scale-A and Scale-B is linear:
\[
B = mA + c
\]
where \( m \) is the slope and \( c \) is the y-intercept.

### Step 2: Calculate the slope \( m \)
The slope \( m \) can be calculated using the two points provided:
\[
m = \frac{B_2 - B_1}{A_2 - A_1} = \frac{54 - 37}{20 - 10} = \frac{17}{10} = 1.7
\]

### Step 3: Determine the y-intercept \( c \)
We can use one of the given points to find \( c \). Using the point \( (A_1, B_1) = (10, 37) \):
\[
37 = 1.7(10) + c
\]
\[
37 = 17 + c
\]
\[
c = 20
\]

### Step 4: Form the equation
Now that we have \( m = 1.7 \) and \( c = 20 \), the relationship between Scale-A and Scale-B is:
\[
B = 1.7A + 20
\]

### Step 5: Calculate the corresponding temperature on Scale-B for \( A = 100 \)
Substitute \( A = 100 \) into the equation:
\[
B = 1.7(100) + 20 = 170 + 20 = 190
\]

Thus, the corresponding measurement on Scale-B for a measurement of 100 on Scale-A is **190**.

Would you like more details or have any other questions?

Here are some related questions:
1. What are the units used for Scale-A and Scale-B?
2. How can you convert temperatures between Fahrenheit and Celsius using a similar linear relationship?
3. If Scale-A and Scale-B were non-linear, how would that affect the relationship?
4. How does the slope affect the rate of change between the two temperature scales?
5. What would the temperature on Scale-A be for a temperature of 200 on Scale-B?

**Tip:** Always check for consistency in the given points when determining the linear relationship to avoid calculation errors.

Understand the linear relationship between Scale-A and Scale-B temperatures with detailed step-by-step solutions. Learn how to calculate temperatures on Scale-B corresponding to Scale-A measurements like 10, 20, and 100. Suitable for Grades 7-9.

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