In order to complete an experiment in chemistry lab, sylvia needs to make a mixture of 130 ml of a 37% base solution from a 67% base solution and a 24% base solution. find the volume of the 67% base solution that sylvia needs to use to make the mixture.
find the volume of the 67% base solution.

The volume of the 67% Base solution is 39.30 mL

Explanation:

Let the volume of 67% base solution used to make the mixture = x mL

Let the volume of 24% base solution used to make the mixture = y mL

Total volume of the mixture = x + y = 130 mL (1)

For 67% base solution:

C₁ = 67% , V₁ = x mL

For 10% base solution:

C₂ = 24% , V₂ = y mL

For the resultant base solution:

C₃ = 37% , V₃ = 50 mL

Using  

C₁V₁ + C₂V₂ = C₃V₃

67×x + 24×y = 37×130

So,  

67x + 24y = 4810 (2)

Solving 1 and 2 we get,

x = 39.30 mL

y = 90.70 mL