I have finished 19 problems but this one is giving me fits! I need to finish it

Question

I have finished 19 problems but this one is giving me fits! I need to finish it in the next few hours so before I go to my second job. The problem is below. Please let me know how much it cost and if can be done in the next couple of hours.

PROBLEM:
You want to take a bath with the water temperature at 35.0°C. The water temperature is 38.0°C from the hot water tap and 11.0°C from the cold water tap. You fill the tub with a total of 185 kg of water. How many kilograms of water from the hot water tap do you use?

Explanation / Answer

Temperature of hot water, t1 = 38 oC

Temperature of cold water, t2 = 11 oC

Temperature of mixture of hot + cold water, t =35 o C

Total mass of mixture , M = 185 kg

Mass of hot water = X

Mass of cold water = 185 - X

Heat loss or gain by water = m S t (where m = mass, S = Specific heat and t = change intemperature )

Heat lost by hot water = Heat gained by coldwater

X * S * ( 38 - 35 ) = ( 195 - X ) * S * ( 35 -11 )

3 X = 24 ( 185 - X )

X = 8 ( 185 - X )

9 X = 8 * 185

Mass of hot water, X = 164.44 kg

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