Alligation / Ratio Question

by Michelle
(IA)

I completed the following problem using the tic tac toe alligation chart, but my answers don't match the answer key. The problem is:

Rx: Prepare 480 mL of a 1:30 solution using a 1:10 solution and a 1:50 solution. What quantities will be used of each stock solution to make the 1:30 solution?

To compute this, I converted the ratios to percentages and used the tic tac toe chart. As a result I got 60 ml for the 10 % solution and 420 ml for the 2% solution. These quantities add up to 480, so I thought I had done the problem right, however the answer is listed as : 78 mL of 1:10, 402 mL of 1:50.

I cannot figure out how they got this answer. Are there steps I need to take beyond the basic alligation chart? Do the ratios change the problem from the basic alligation problem? I'm so confused.