Rajan needs 1 liter of 15% hydrochloric acid solution for an experiment. he checks his storage cabinet, but he only has a 5-liter bottle of 5% hydrochloric acid solution and a 1-liter bottle of 45% hydrochloric acid solution. how many liters of the 5% hydrochloric acid and the 45% hydrochloric acid solutions should rajan combine to make 1 liter of a solution that is 15% hydrochloric acid?

Rajan must use 0.75 liters of 5% hydrochloric acid solution and 0.25 liters of 45% hydrochloric acid solution.

Step-by-step explanation:

Let us assume that, x liters of the 5% hydrochloric acid and y liters of the 45% hydrochloric acid solutions are combined.

As Rajan need total of 1 liter of solution, so

i.e --------------------1

As Rajan needs 5% hydrochloric acid and 45% hydrochloric acid to make a 1 liter batch of 15% hydrochloric acid, hence acid content of the mixture of two acids will be same as of the final one, so

i.e -------------2

Putting value of x from equation 1 in equation 2,

Putting the value of y in equation 1,

Therefore, Rajan must use 0.75 liters of 5% hydrochloric acid solution and 0.25 liters of 45% hydrochloric acid solution.

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.