A researcher orders a broth of 8% glucose for her lab. However, she needs a stronger broth,one that is 14.1% glucose. Fortunately, she has 70.6 liters of 41% glucose broth in the stock room. How much 14.1% glucose can she make?
What she has are two containers each containing some glucose
mixed with water, One is too strong and the other is too weak,
so she wants to add enough of the weak to all of the strong
to dilute it down to the medium strength that she wants.
Let the amount of the weak that she needs to add to the strong
be x liters.
We make this chart:
liters of liquid | strength | liters of pure glucose in the liquid
---------------------------------------------------------------------------
strong | |
weak | |
medium | |
We have 70.6 liters of liquid of the strong and we add x liters of
liquid of the weak so we will end up with (70.6 + x) liters of the
medium strength we want.
So we fill in the first column, which is the number of liters of liquid
of the strong and of the weak, and the final amout of liquid of medium
strength that we want to end up with. We also fill in the middle
column with the three strengths.
liters of liquid | strength | liters of pure glucose in the liquid
---------------------------------------------------------------------------
strong 70.6 | 41% |
weak x | 8% |
medium 70.6 + x | 14.1% |
Then we fill in the liters of pure glucose contained in each
liters of liquid | strength | liters of pure glucose in the liquid
---------------------------------------------------------------------------
strong 70.6 | 41% | .41(70.6)
weak x | 8% | .08x
medium 70.6 + x | 14.1% | .141(70.6 + x)
Liters of pure Liters of pure Liters of pure
glucose in the + glucose in the = glucose in the
strong weak medium
.41(70.6) + .08x = .141(70.6 + x)
Solve that and get x = 53.8527541 liters of weak that she needs to
add to the strong solution to dilute it down to the medium strength she
wants.
Edwin