Question #c47d5

Aug 13, 2017

He needs 10 ml of the 30% solution, and 90 ml of the 10% solution. This will create 100 ml of 12% solution.

Explanation:

This is basically a system of equations problem. You can set it up like this:

Let x represent the amount of 30% solution needed and let y represent the amount of 10% solution needed

$0.3 x + 0.1 y = 12$
$x + y = 100$

We know that 30% of x added to 10% of y must give us 12 ml of the acid. We also know that x and y must add to 100. Those are represented above.

Now you can use substitution to solve. In the second equation, x+y=100, we can solve for x to get x = 100 - y. Then if we sub that in to the first equation, we can solve:

$0.3 x + 0.1 y = 12$
$0.3 \left(100 - y\right) + 0.1 y = 12$

$30 - 0.3 y + 0.1 y = 12$

$30 - 0.2 y = 12$

$- 0.2 y = - 18$

$y = 90$

We need 90 ml of the 10% solution, meaning we must need 10 ml of the 30% solution.