I use a
diagram to help set up the equation. The
diagram looks like this. % (amount) +
% (amount) = % (total amount) A chemist need to mix the of70% solution should be used?[Note: I have colored coded some of the key elements of
this problem to help you set up the problem “with me”.] First always
identify, what we are trying to find. The
question asks … solution … so we begin with of
70%x = the amount of70%The first
pieces of information that I look for in the problem are the percentages. You need to fill these in the diagram in the
appropriate places. You really shouldn’t
have too much trouble doing this especially if you remember that the “middle”
value percentage has to be on the right-hand side of the equation (resultant mixture). In other words, in our problem we have percentages
of 40, 50, and 70 … 50 is the (numerical) median and therefore is on the
“right-hand” side of the equation. Fill in the
percentages now.
Next try and
determine any given amounts. The problem
links the amounts to the percentages
may often be interpreted as multiplication. This
particular problem states that we have of20 liters of40%, so 20 is
the amount linked to 40% by multiplication. Also, the question asks liters How many%
(in the problem it also says we have “of 70some”
70% … this means we have an unknown.) and
therefore the variable x is the amount of70%.Fill in this
information.
40
40 Now, we
still need one more piece of information … the
Now we need
to solve the equation.
So the
amount of 70% needed is 10 Liters. Let’s
try another problem similar to that problem.
12% solution must be
mixed with a 20% solution to get 10 gallons
a of14% solution?If we let
Notice that
we identified the amount of [Think about
it … Now, to
solve the equation:
– 8x = – 60
x = 7.5
gallons of 20%
The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was edited on 19-Sep-2007 |