a group of chemists are conducting an experiment to produce a new liquid material. One chemical contains 15% sodium and the other chemical contains 30% sodium. Once they mix the two samples the resulting chemical contains 22% sodium. How many mililiters of each sample must be mixed to obtain 600ml of the new chemical?
You always want to try and identify the quantities you're being asked to find and give them letters. In this case, you're being asked for the number of millilitres of solution 1: call this X; and the number of millilitres of solution 2: call this Y. One piece of data is that the total, X+Y, is 600. You now have to use the rest of the data to get another relationship between X and Y. The amount of sodium in the mixture is 15% of X plus 30% of Y, which is 15X/100 + 30Y/100. You're told that this is equal to 22% of the total, that is 22% of X+Y or 22(X+Y)/100. So we have two equations, X+Y = 600 and 15X/100 + 30Y/100 = 22(X+Y)/100. Solve as a pair.
Originally Posted by rgep
I still don't get it. when you start putting in the 100 I understand that it is because 100% but then I get lost when it comes to all the multilying and dividing I have tried to get this can u explain step by step how to come up with this answer
Solution 1, with 15% sodium: we call that X
Solution 2, with 30% sodium: we call that Y
Volume: Solution 1 and Solution 2, you get the new volume as 600mL.
X + Y = 600 ----- (i)
Sodium concentration in Solution 1 (15%) and sodium concentration in Solution 2 (30%) adds up to sodium concentration in the final solution (22%).
So it means:
15%X + 30%Y = 22%*(X+Y) ----- (ii)
Substitute (ii) into (i)
15%X + 30%Y = 22%*600
Then rewrite it as
15X/100 + 30Y/100 = 22*600/100
Simplify it into:
15X + 30Y = 22(600)
15 (X + 2Y) = 22*600/15
X + 2Y = 880 ----- (iii)
From (i)
X + Y = 600
Y = 600-x -----(iv)
Substitute (iv) into (iii)
X + 2Y = 880
X + 2*(600-X) = 880
X + 1200 - 2X = 880
X = 320 (Solution 1)
Therefore
X + Y = 600
320 + Y = 600
Y = 280 (Solution 2)
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