how many ounces of 30% vitamin C solution should be mixed with a 10% by vitamin solution to make 50 ounces of a 25% vitamin solution

Question

I don't quite understand how to do this problem and when I try I get a invalid answer

Answer 1

Hi Nicole!

 

Let x = the number of ounces of the 30% vitamin C solution

     y = the number of ounces of the 10 vitamin C solution

 

The total number of ounces of the mixed solution is 50 ounces. Thus,

 

x+y = 50

 

When we focus on the content of the solution, we know that x is 30% vitamin C, and y is 10% vitamin C, and the total is 25% vitamin C. Thus,

 

0.30x + 0.10y = 0.25 (50), which can be written as 0.30x + 0.10y = 12.5

 

Now we do have two equations with two unknowns. We put the equations in a simultaneous equation form and then solve them accordingly. Hence, 

 

x+y = 50

0.30x + 0.10y = 12.5.

 

To simplify the computation let's multiply the second equation by 10 so that the decimals will be integers. Therefore, we will have 3x + 1y = 125. Thus, we have

 

3x + y = 125

x+y = 50

 

Subtract the second equation from the first

 

2x = 75

x = 37.5 ounces. 

 

Accordingly, y = 12.5 ounces (50 - 37.5)

 

I hope it helps.

A.