Solving Physics Problem: Hot & Cold Liquids w/Formulas

[Zygotic Embryo]

Hello, I am just starting Physics. ( Sophmore in high school)

I need some help, understanding and solving this problem.


When you mix hot and cold liquids you can find the temperature of the mixture by using the formula T= ah+bc divided by a+b, where T is the temperature of the mixture, h is the temperature of the hot liquid, c is the temperature of the cold liquid, a and b respresent the amounts of hot and cold liquids. Suppose you mix hot tea and cold milk in a ratio a:b of 9:1 and find that the temperature of the mixture is 117degrees You then change the trea:milk ratio to 2:1 and the temperature drops 96degrees. Find the initial temperatures of the tea and Milk.

Again, I can solve it Logically. But using Formula's ( showing your work ) I am not very found of..

Can someone show how to go about this. Thanks!

 

[Mk]

Can't you solve it using simple algebra?

For your first ratio, you would just plug in your values, and it would look something like this:

117=(9h/10)+(c/10)
for the second:
96=(2h/3)+(c/3)

Simplify them and work them out separately, until you have both of the variables (h and c) on one side for both equations.

You can then have "h" equal something ±c, then in the second equation inject what h equals into h's place. Solve the equation for c, then solve the first equation as you would a one-variable algebraic equation.