Simple Physics.

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

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!


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:

for the second:

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.
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