hey guys need help:

Alan needs a 250 ml of solution that is 45% alcohol. If he has a solution that is 50% alcohol and purified water (which is 0% alcohol), how much of each should he use?
Be sure to define each variable. Write a system of equations. Solve.

Abdul wants 50 pounds of tea that he can sell for $5.14 per pound. If he has tea that costs $7.80 per pound and tea that costs $4.30 per pound, how much of each should he use?
Be sure to define each variable. Write a system of equations. Solve.

Both of the problems are very similar. I will solve one for you; you may want to try the second by yourself. If you still do not get it, I can help you again.

The amount of alcohol in 250 solution = 45%
Say, total quantity = X
45% of X = 112.50 mL

But the solution has got only 50% of alcohol, so 2 * 112.50 = 225
The amount of wate = 250 - 225 = 25 mL

MY Solution that is very easy to understand:
Let he has to take X ml of alcoholic solution and Y ml of water.

now we need two equations involving X and Y to solve it.

First equation:
The final volume should be 250ml. Hence X + Y = 250

Second equation:
The percentage of alcohol in the final solution should be 45. Hence:

Volume of Alcohol / Total volume of solution = 0.45

(X/2) / ( X +Y) = 0.45

( because, when we take total X alcoholic water, it will have only X/2 alcohol in it).


Solving these two equations you get X = 225 ml and Y = 25 ml

Cheers.

i need some equations. i think kapuri kha's soln looks nice for me.
thank you slackdemic.
thank you kapuri kha.