Question

One winter night the temperature fell 14 degrees between midnight and 5 am. by 9 am the temperature had doubled from what it was at 5 am. by noon, it had risen another 8 degrees to 32 degrees. what was the temperature at midnight?

Answer 1

The temperature at midnight was 26 degrees.

Explanation:

Let "x" be the temperature in midnight.

The temperature fell 14 degrees by 5 am.

Temperature at 5 am = x - 14

Temperature at 9 am doubled from what it was at 5 am.

So, temperature at 9 am = 2(x - 14)

It had risen another 8 degrees to 32 by noon.

So, temperature at noon

32 = 2(x - 14) + 8

Now we have to find the value of x.

Distribute 2 inside the parenthesis, we get

32 = 2x - 28 + 8

32 = 2x - 20

2x = 32 + 20

2x = 52

Dividing both sides by 2, we get

`(2x)/(2) = (52)/(2)`

x = 26

Therefore, the temperature at midnight was 26 degrees.

Answer 2

Temp 5.00 = Tm - 14

Temp 9.00 = 2 (Tm -14)

Temp noon = 8 +2 (TM - 14)

32 = 8 + 2 TM - 28
52 = 2 TM
Tm = 26

Hope this helps