SOLUTION: I have 32 fluid ounces of a 3% solution and 32 fluid ounces of a 35% solution. How many ounces of each will I have to add together to make 32 fluid ounces of a 4% solution?

Algebra ->  Equations -> SOLUTION: I have 32 fluid ounces of a 3% solution and 32 fluid ounces of a 35% solution. How many ounces of each will I have to add together to make 32 fluid ounces of a 4% solution?       Log On


   

Question 1153594: I have 32 fluid ounces of a 3% solution and 32 fluid ounces of a 35% solution. How many ounces of each will I have to add together to make 32 fluid ounces of a 4% solution?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
v, the volume of 35%
32-v, volume of the 3%

35v%2B3%2832-v%29=4%2A32
Solve. Algebra steps first. Computation later.

35v%2B3%2A32-3v=4%2A32
35v-3v=4%2A32-3%2A32
v%2835-3%29=32%284-3%29
v=32%28%284-3%29%2F%2835-3%29%29
highlight_green%28v=32%281%2F32%29=1%29=1


---------------------OR MUCH QUICKER---------------------------------------------
highlight_green%2835v%2B3%2A32-3v=4%2A32%29
32v=4%2A32-3%2A32
highlight%28v=32%2F32%29-------------meaning 1 fluid ounce of the 35%, and 31 fluid ounce of the 4%.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor showed how to set up the problem for solving using the standard algebraic method. If an algebraic method is not required, here is a solution by a method that will get you to the answer much faster, and with far less work.

Think of starting with 3% solution and adding 35% solution, stopping when you get to 4%.

To model that, think of "walking" along a number line, starting at 3 and heading towards 35, stopping when you get to 4. From 3 to 4 is 1/32 of the distance from 3 to 35.

That means 1/32 of the mixture needs to be the 35% solution you are adding.

Since you want 32 fl oz of the mixture, that means you need to use 1 fl o of the 35% solution and 31 fl oz of the 3% solution.

Without all the words of explanation, here are the simple calculations required to solve the problem.

4-3=1; 35-3=32 --> 1/32

(1/32) of 32 fl oz = 1 fl oz = amount of 35% solution to use