Question

How many milliliters of the 40% solution should she add to the 10% solution to get this concentration?
mL

Answer 1

I don't have the full numbers (how much of the 10% solution she has and what final percent she wants). Could you give those?

Meanwhile, here is the general method and formula you can use.

Let:
- y = mL of the 10% solution she starts with,
- x = mL of the 40% solution to add,
- c = desired final concentration (as a decimal, e.g. 25% = 0.25).

Set up the percent-by-volume equation for the pure solute:
0.10·y + 0.40·x = c·(x + y).

Solve for x:
x = [(c − 0.10) / (0.40 − c)] · y.

Notes:
- This formula is valid only if 0.10 < c < 0.40 (final concentration must be between the two given concentrations).
- If you give y and c I can compute the numeric value. Example: if y = 100 mL and c = 25% (0.25), then x = [(0.25−0.10)/(0.40−0.25)]·100 = (0.15/0.15)·100 = 100 mL.