Solving Word Problems With Equations Of One Degree And One Unknown Worksheet With Answers Page 19
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202. How many pounds of nuts at 63¢ per lb. should be mixed with 20 lbs. of nuts at 90¢
per lb. to give a mixture worth 78¢ per lb.? (HINT: The principle is the same; the cost
per lb. replaces the percent in the diagram.)
let x = # of pounds of .63 per lb. nt.wt.
Amount
value per lb.
total
63
X
63
63x
1800
90
20
90
mixture 78
20 + x
78
78(20 + x)
78(20 + x) = 1800 +63x
x = 16
3. A druggist needs 20ml. of a 30% solution. To obtain this he mixes an 80% stock of
the solution with a diluent (0% solution). How many ml. each, of the stock and the
diluent should be mixed? (HINT: Don’t let the 0% confuse you. Use it and the
problem will work!)
Let x=#ml. of 80% solution.
Amount
rate
concentration
80%
X
.80
.8x
diluent
20-x
0
0
final solution 30%
20
.30
20(.3)=6
.8x+0=6
.8x=6
x=7.5ml.
7.5 ml. of 80% solution must be mixed by 12.5 (20-7.5) ml. of diluent to obtain 20ml.
of 30% solution.
WORK PROBLEMS
1. JoAnn requires 20 hours to complete a certain job and Wanda will require 30 hours to
do the same job. How long will it take JoAnn and Wanda working together to do the
job?
Let x=time required working together
Rate
time
part done
Joann
1/20
x
x/20
Wanda
1/30
x
x/30
1
x/20+x/30=1
LCD=60
60(x/20)+60(x/30)=60(1)
3x+2x=60
x=12
19
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