Question

The mean room temperature from Monday to Saturday is 25oC and the mean room temperature of Saturday and Sunday is 28oC. if the mean room temperature from Monday to Sunday is 26oC, find the room temperature on Saturday

Answer 1

We can conclude that the room temperature on Saturday was 24°C

Explanation:

For a set of N values:

{x₁, x₂, ..., xₙ}

The mean of the set is calculated as:

`M = (x_1 + x_2 + ... + x_n)/(N)`

In this case, our set is the temperature of 7 days (so we have 7 elements)

{T₁, T₂, T₃, T₄, T₅, T₆, T₇}

Such that:

T₆ = temperature on Saturday

T₇ = temperature on Sunday.

We know that:

"The mean room temperature from Monday to Saturday is 25°C"

Then:

`(T_1 + T_2 + T_3 + T_4 + T_5 + T_6)/(6) = 25 C`

"the mean room temperature of Saturday and Sunday is 28°C"

`(T_6 + T_7)/(2) = 28C`

"The mean room temperature from Monday to Sunday is 26°C"

`(T_1 + T_2 + T_3 + T_4 + T_5 + T_6 + T_7)/(7) = 26 C`

So we have 3 equations.

Let's rewrite:

T₁ + T₂ + T₃ + T₄ + T₅ = A

Then we can rewrite our equations as:

`(A+ T_6)/(6) = 25 C`

`(T_6 + T_7)/(2) = 28C`

`(A + T_6 + T_7)/(7) = 26 C`

Removing the "Celcius" and multiplying in the 3 equations by the denominator on both sides, we get:

A + T₆ = 6*25

T₆ + T₇ = 2*28

A + T₆ + T₇ = 7*26

We now need to solve that system for T₆

The first step is to isolate one of the variables in one of the equations, (because we want to solve this for T₆ , let's not isolate that one). Let's isolate A in the first one:

A = 6*25 - T₆

A = 150 - T₆

Now we can replace this on the other two equations:

T₆ + T₇ = 2*28

(150 - T₆ ) + T₆ + T₇ = 7*26

Now, let's isolate T₇ in the top equation to get:

T₇ = 2*28 - T₆

T₇ = 56 - T₆

Now we can replace this in the last equation to get:

(150 - T₆ ) + T₆ + (56 - T₆) = 7*26

Now, we can solve this for T₆

150 - T₆ + T₆ + 56 - T₆ = 182

-T₆ = 182 - 150 - 56

-T₆ = -24

T₆ = 24

We can conclude that the room temperature on Saturday was 24°C