How many milliliters of 0.30% sugar solution must you add to 75mL of 4% sugar solution to get a 0.50% sugar solution?

Question

kash_thesmartguy · Answer

Please post it in Chemistry. This is math.

anonymous · Answer

but this is a math problem, I'm supposed to use rational functions to solve it

mathstudent55 · Answer

75 ml of a 4% solution of sugar has 0.04(75 ml) amount of sugar.
You are adding x ml of the 0.50% solution to it.
How much sugar is there in x ml of 0.50% solution?

anonymous · Answer

.005x ml of sugar in the 0.50% solution

anonymous · Answer

ok

mathstudent55 · Answer

You need to add x amount of the 0.3% solution.
In x ml of solution, the 0.3% solution has 0.003x amount of sugar.
Ok?

anonymous · Answer

ok

mathstudent55 · Answer

Now when you add the 75 ml of solution to x ml of 0.3% solution, the amount of sugar will be:

$3 + 0.003x$

Right?

anonymous · Answer

why is it 3?

mathstudent55 · Answer

4% * 75 ml = 3 ml (this amount of sugar comes from the 4% solution.)
0.003x (this amount of sugar comes from the 0.3% solution)
We add the sugar, and we get:

$3 + 0.003x$

anonymous · Answer

okay I understand now

anonymous · Answer

4% * 75 ml = 3 ml (this amount of sugar comes from the 4% solution.)
0.003x (this amount of sugar comes from the 0.3% solution)
We add the sugar, and we get:

3+0.003x 

yup he is  correct 

next time post in chemestry though but i understand why you did it in math

mathstudent55 · Answer

The concentration of sugar is the amount of sugar divided by the total volume.

We divided the amount of sugar, 3 + 0.003x by x + 75 and we want that to be 0.5%

$\dfrac{3 + 0.003x}{75 + x} = 0.005$

mathstudent55 · Answer

This is a math problem that can very well be in a math book under rational equations.

anonymous · Answer

ok

anonymous · Answer

The concentration of sugar is the amount of sugar divided by the total volume.

We divided the amount of sugar, 3 + 0.003x by x + 75 and we want that to be 0.5%

3+0.003x/75+x =0.005  

do you get it

mathstudent55 · Answer

math deals with many situations, such as concentrations of solutions.

anonymous · Answer

yeah, I get that

mathstudent55 · Answer

Now you solve the equation to find x, the volume of the 0.3% solution needed.

anonymous · Answer

I got x=1,312.5 
Is that correct?

mathstudent55 · Answer

Yes!
Great job!

anonymous · Answer

oh! ok, thanks so much

mathstudent55 · Answer

You're welcome.