Usually, these exercises
are fairly easy to solve once you've found the equations. To help you
see how to set up these problems, below are a few more problems with their
grids (but not solutions).
How many liters
of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution?
liters
sol'n
%
alcohol
total
liters alcohol
70% sol'n
x
0.70
0.70x
40% sol'n
50
0.40
(0.40)(50)
= 20
50% mix
50
+ x
0.50
0.50(50
+ x)
From
the last column, you get the equation 0.7x + 20 = 0.5(50 + x).
Solve for x.
How many ounces
of pure water must be added to 50 ounces of a 15% saline solution to make a saline solution that is 10% salt?
ounces
liquid
%
salt
total
ounces salt
water
x
0
0
15% sol'n
50
0.15
(50)(0.15)
= 7.5
10% mix
50
+ x
0.10
0.10(50
+ x)
From the last column, you
get the equation 7.5
= 0.1(50 + x).
Solve for x.
(Note
the percentage for water. "Pure water" contains no salt, so
the percent of salt is zero. If, on the other hand, you were trying to
increase the salt content by adding pure salt, the percent would have
been one hundred.)
Find the selling
price per pound of a coffee mixture made from 8 pounds of coffee that sells for $9.20 per pound and 12 pounds of coffee that costs $5.50 per pound.
How many pounds
of lima beans that cost $0.90 per pound must be mixed with 16 pounds of corn that costs $0.50 per pound to make a mixture of vegetables that costs $0.65 per pound?
pounds
$/pound
total
$ for veggies
lima
beans
x
$0.90
$0.90x
corn
16
$0.50
(16)($0.50)
= $8
mix
16
+ x
$0.65
(16
+ x)($0.65)
From
the last column, you get the equation $0.90x + $8 = (16 + x)($0.65).
Solve for x.
Two hundred liters
of a punch that contains 35% fruit juice is mixed with 300 liters (L) of another punch. The resulting
fruit punch is 20% fruit juice. Find the percent of fruit juice in the 300 liters of punch.
liters
punch
%
juice
total
liters juice
35% juice
200
0.35
(200)(0.35)
= 70
other
punch
300
x
300x
mix
200
+ 300 = 500
0.20
(500)(0.20)
= 100
From
the last column, you
get the equation 70 + 300x = 100. Solve for x,
and then convert the decimal answer to a percentage.
Ten grams of
sugar are added to a 40-g
serving of a breakfast cereal that is 30% sugar. What is the percent concentration of sugar in the resulting mixture?
grams
in bowl
%
sugar
total
grams sugar
sugar
10
1.00
10
cereal
40
0.30
(40)(0.30)
= 12
mix
50
?
10
+ 12 = 22
From the last row, you
see that there are 22 grams of sugar in the 50 grams in the bowl, or ^{22}/_{50}.
Simplify, and then convert to a percentage.