The average temperature for Wednesday, Thursday, and Friday was 40°C. The average for Thursday, Friday, and Saturday was 41°C. If the temperature on Saturday was 42°C, what was the temperature on Wednesday?

Question

The average temperature for Wednesday, Thursday, and Friday was 40°C. The average for Thursday, Friday, and Saturday was 41°C. If the temperature on Saturday was 42°C, what was the temperature on Wednesday?

A. 39°C
B. 44°C
C. 38°C
D. 41°C

Core Concept

The core concept being tested is Averages. Specifically, the problem involves calculating an unknown temperature using the relationship between multiple averages.

Definition of Average:

The average of a set of numbers is calculated by dividing the sum of those numbers by the total number of elements in the set. In this case, we’re dealing with averages of temperatures over a few days.

$$\text{Average} = \frac{\text{Sum of temperatures}}{\text{Number of days}}$$

Step-by-Step Solution

Step 1: Define the Variables

Let:

• $W$ represent the temperature on Wednesday.
• $T$ represent the temperature on Thursday.
• $F$ represent the temperature on Friday.
• $S$ represent the temperature on Saturday.

Step 2: Use the Average for Wednesday, Thursday, and Friday

We are told that the average temperature for Wednesday, Thursday, and Friday is 40°C:

$$\frac{W + T + F}{3} = 40$$

Multiplying both sides by 3:

$$W + T + F = 120 \quad \text{(Equation 1)}$$

Step 3: Use the Average for Thursday, Friday, and Saturday

We are also told that the average temperature for Thursday, Friday, and Saturday is 41°C:

$$\frac{T + F + S}{3} = 41$$

Multiplying both sides by 3:

$$T + F + S = 123 \quad \text{(Equation 2)}$$

Step 4: Substitute the Known Value for Saturday

We are given that the temperature on Saturday was 42°C, so $S = 42$. Substituting $S = 42$ into Equation 2:

$$T + F + 42 = 123$$

Simplifying:

$$T + F = 123 – 42 = 81 \quad \text{(Equation 3)}$$

Step 5: Substitute Equation 3 into Equation 1

Now, substitute $T + F = 81$ from Equation 3 into Equation 1:

$$W + (T + F) = 120$$

Substitute $T + F = 81$:

$$W + 81 = 120$$

Step 6: Solve for $W$

Now, solve for $W$:

$$W = 120 – 81 = 39$$

So, the temperature on Wednesday was 39°C.

Correct Answer and Option

The temperature on Wednesday was 39°C.

Correct Answer: A

Answer Reasoning

By carefully setting up the two equations based on the average temperatures for Wednesday to Friday and Thursday to Saturday, and substituting the given temperature for Saturday, we were able to solve for the unknown temperature on Wednesday. The final calculation gives us 39°C, which is the correct answer.

Explanation of Incorrect Options

• Option B (44°C): This is incorrect because the sum of the temperatures required to make this option true would exceed the given averages, leading to an impossible situation.
• Option C (38°C): This is incorrect because it would not satisfy the given conditions. Substituting 38°C would result in values inconsistent with the averages provided.
• Option D (41°C): This is incorrect because substituting 41°C as the temperature for Wednesday would not result in the correct sums for the averages.

Common Mistakes to Avoid

1. Incorrectly Substituting Values: Be sure to substitute the values accurately and work with the correct relationships between the variables.
2. Misunderstanding Averages: Remember that the average is the sum of values divided by the number of terms. Ensure that you’re setting up the equation correctly.

Simplest Way to Solve (Shortcut or Insight)

The most efficient way to solve this problem is to use the relationship between the sums of temperatures. Write two equations based on the averages, substitute the known value for Saturday’s temperature, and then solve the system of equations. This eliminates unnecessary steps and leads to the solution quickly.

Visual Aid Suggestion

A simple table or diagram could be useful to visualize the relationships between the temperatures for each day. You could set up a table where each row represents a day and each column shows the sum of temperatures for the relevant days. This can help ensure the correct values are substituted and can make it easier to visualize the arithmetic involved.

Practice Questions

1. Question 1:
   The average of the temperatures for Monday, Tuesday, and Wednesday is 30°C. The average for Tuesday, Wednesday, and Thursday is 32°C. If the temperature on Thursday is 34°C, what was the temperature on Monday?
   A. 28°C
   B. 30°C
   C. 32°C
   D. 34°C
   (Answer: A)
2. Question 2:
   The average temperature for three consecutive days is 27°C. The temperature on the first day was 25°C, and the temperature on the third day was 28°C. What was the temperature on the second day?
   A. 29°C
   B. 27°C
   C. 30°C
   D. 26°C
   (Answer: B)
3. Question 3:
   The average temperature of the first four days of a week is 34°C. If the temperature on the fifth day is 38°C, what is the new average for all five days?
   A. 35°C
   B. 36°C
   C. 37°C
   D. 38°C
   (Answer: A)
4. Question 4:
   The average of five numbers is 18. If the first four numbers are 15, 20, 16, and 22, what is the fifth number?
   A. 16
   B. 17
   C. 18
   D. 19
   (Answer: B)
5. Question 5:
   The average of five consecutive odd numbers is 35. What is the middle number?
   A. 33
   B. 35
   C. 37
   D. 39
   (Answer: B)