Solving Word Problems With Equations Of One Degree And One Unknown Worksheet With Answers Page 10
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20+ or -
=
=
%
%
%
!
!
!
Go back and reread the problem. We are asked to find how many liters of each
!
solution (60% and 15%) we need to mix. We don’t know any more about one of
them than the other. So we call the number of liters of the 60% solution “X”. To
represent the numbers of liters of the 15% solution we use the WHOLE-PART
hint at the end of the investment problems. We want to end up with 82.5 liters.
This represents the whole. We denote one part by “X”. The other part is 82.5 - X.
Now we can complete more of the diagram.
!
82.5 - X
X
82.5
+
=
15
60%
20%
%
Note that the sum of 60% and 15% DOES NOT EQUAL 20%. But the sum of “X”
and “82.5 - X” DOES EQUAL 82.5. This should always be true on your diagram.
(Remember that a 50% acid solution means that 50% of the liquid is acid.)
Remember, too, that “of” means multiply. In the case at hand, then, we are speaking
of 60% of X liters, 15% of 82.5 - X liters and 20% of 82.5 liters. So, we translate this
into an equation:
.60X + .15(82.5 - X) = .20(82.5)
Solve the equation. First multiply each term by 100 to get rid of the decimals.
!
60X + 15(82.5-X) = 20(82.5)
60X + 1237.5 – 15X = 1650
45X + 1237.5 = 1650
45X = 412.5
X = 9.17 or 9 1/6
The problem asked for the number of liters of each solution. We let X = the
!
number of liters of the 60% solution, so we need 9.17 liters of that solution. We
let 82.5 - X = the number of liters of the 15% solution. Substituting X in the
equation we get 82.5 – 9.17 = 72.33 liters of that the 15% solution.
PROBLEM SOLVING
1. A tank contains 10,000 gallons solution that is 5 percent sodium chloride by
volume. If 2,500 gallons of water evaporate from the tank, the remaining
solution will be approximately what percent sodium chloride?
a) 1.25%
b) 3.75%
c) 6.25%
d) 6.67%
e) 11.7%
Answer D
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