A skin care cream is made with vitamin c. How many ounces of a 30% vitamin c solution should be mixed with a 10% vitamin c solution to make 50 ounces of a 25% vitamin c solution?

Let x be the number of ounces of 30% vitamin C solution and let y be the number of ounces of 10% vitamin C solution that are needed to make 50 ounces of a 25% vitamin C solution.

x + y = 50 ... (1)

y = 50 - x ... (2)

0.3x + 0.1y = 0.25 * 50 ... (3)

Plugging the expression for y in (2) into (3), we get:

0.3x + 0.1 (50 - x) = 12.5 ... (4)

Expanding and simplifying (4) we get:

0.2x = 7.5

x = 37.5 ... (5)

Plugging the value of x in (5) into (2), we get:

y = 50 - 37.5 = 12.5

The answer is: 37.5 ounces of 30% vitamin C solution and 12.5 ounces of 10% vitamin C solution.