Carbon Black Nickel |

Carbon Black Nickel

Carbon Black Nickel

I NEED MATH HELP. GREATLY NEEDED.?

okay so now i need these two things answered.
i'm extremely confused.
please explain and include equations.

1."Sulfuric acid can be used to remove water from organic materials leaving behind a residue of black carbon. If beaker 2 contains a 15% soulution of sulfuric acid and break b contains 20% soulution of sulfuric acid, how much can each beaker should beused to make 6 liters of an 18% soulution of sulfric acid?"

2. "How many mg of metal containing 45% nickel much be combined with 6 mg of pure nickel to form an alloy containing 78% nickel?"

Now, I need the mathemetical answers, not science.
I'm a freshman in high school, so its nothing fancy.
Please PLEASE Please help.
I need it very badly.
I will be forever greatful.
I will award a best answer too (:

These are systems.

1) let x be the amount needed from beaker 1
let y be the amount needed from beaker 2.

the final solution is 6 liters, so:
x + y = 6
15% of the amount in beaker 1 (x) is sulfuric acid.
20% of the amount in Beaker 2 (y) is sulfuric acid, and
18% of the amount in the final Beaker(6L) is sulfuric acid. So, adding the components gives you the end result:
15%x + 20%y = 18%(6)
change percent to decimals:
0.15x + 0.2y = 0.18(6)

now just solve this system:
x + y = 6
0.15x + 0.2y = 0.18(6)

I would use elimination. multipy the second equation by 5 and subtract the two equations:
x + y = 6
0.75x + y = 0.18(30)
0.25x = 6 - 0.18(30) = 0.6
x = 3.6 (liters from Beaker 1)
y = 2.4 (liters from Beaker 2)

2) Use the same concept:
let x be mg of 45% nickel.
let y be mg of 78% nickel

This time, you know one of the components (6mg of pure), so:
x + 6 = y
and
0.45x + 1.00(6) = 0.78y
(because pure = 100% = 1.00)

solve the two equations.
substitution y:
0.45x + 1.00(6) = 0.78(x + 6)
0.45x + 6 = 0.78x + 4.68
1.32 = 33x
x = 25 (mg of 45% nickel)