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.
