The average temperature of Monday, Tuesday , Wednesday and Thursday is 60°. The average temperature for Tuesday, Wednesday, Thursday and Friday is 63°. If the ratio of temperature for Monday and Friday is 21 : 25, then what is the temperature of Friday?

Options

A. `70^(@)`
B. `73^(@)`
C. `75^(@)`
D. `78^(@)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the variables
Let the temperatures for Monday, Tuesday, Wednesday, Thursday, and Friday be represented as:
- \( M \) = Temperature on Monday
- \( T \) = Temperature on Tuesday
- \( W \) = Temperature on Wednesday
- \( R \) = Temperature on Thursday
- \( F \) = Temperature on Friday

### Step 2: Set up the equations based on the averages
From the problem, we know:
1. The average temperature of Monday, Tuesday, Wednesday, and Thursday is 60°:
\[ \frac{M + T + W + R}{4} = 60 \]
Multiplying both sides by 4 gives:
\[ M + T + W + R = 240 \quad \text{(Equation 1)} \]

2. The average temperature for Tuesday, Wednesday, Thursday, and Friday is 63°:
\[ \frac{T + W + R + F}{4} = 63 \]
Multiplying both sides by 4 gives:
\[ T + W + R + F = 252 \quad \text{(Equation 2)} \]

### Step 3: Use the ratio of temperatures
We are given that the ratio of the temperature on Monday to the temperature on Friday is 21:25. This can be expressed as:
\[ \frac{M}{F} = \frac{21}{25} \]
From this, we can express \( M \) in terms of \( F \):
\[ M = \frac{21}{25}F \quad \text{(Equation 3)} \]

### Step 4: Substitute Equation 3 into Equation 1
Substituting \( M \) from Equation 3 into Equation 1:
\[ \frac{21}{25}F + T + W + R = 240 \]
Multiplying the entire equation by 25 to eliminate the fraction:
\[ 21F + 25T + 25W + 25R = 6000 \quad \text{(Equation 4)} \]

### Step 5: Substitute Equation 1 into Equation 2
Now, we can express \( T + W + R \) from Equation 1:
\[ T + W + R = 240 - M \]
Substituting \( M \) from Equation 3:
\[ T + W + R = 240 - \frac{21}{25}F \]
Now substitute this into Equation 2:
\[ (240 - \frac{21}{25}F) + F = 252 \]
Combining terms:
\[ 240 - \frac{21}{25}F + F = 252 \]
Converting \( F \) to a fraction:
\[ 240 - \frac{21}{25}F + \frac{25}{25}F = 252 \]
This simplifies to:
\[ 240 + \frac{4}{25}F = 252 \]

### Step 6: Solve for \( F \)
Subtract 240 from both sides:
\[ \frac{4}{25}F = 12 \]
Now, multiply both sides by \( \frac{25}{4} \):
\[ F = 12 \times \frac{25}{4} = 75 \]

### Conclusion
The temperature on Friday is:
\[ \boxed{75} \]