Let x represent the amount of 10% solution used. Let y represent the amount of 25% solution used.
Since 30 liters of 15% solution are being made, our first equation is x + y = 30
Now we deal with the actual peroxide in each solution. x liters of 10% peroxide contain 0.1x liters of peroxide. y liters of 25% peroxide contain 0.25y liters of peroxide. 30 liters of 15% peroxide contain 0.15 * 30 = 4.5 liters of peroxide. From this information, we can write our second equation.
0.1x + 0.25y = 4.5
We have a system of equations:
x + y = 30 0.1x + 0.25y = 4.5
Multiply the first equation by -0.25 and add to the second equation.
Both are the same because the first line is going by ×2 so the missing number would be 22. The second line is going by +1 so 21+1=22. (Hope this will prove your friend wrong :3)
If we know that 6 things cost 2.99 and we want to know unit price we just have to divide 2.99 by 6. So 2.99:6=0.49$ - its the result. Now we can say that his sister is not correct, because price is different that 2$/unit.
