Take Me Out to the Ballgame Mixture Problems in 2 Variables.
Mixture Problems 2
22
Mixture Problems (part 2)
Transcript of Mixture Problems 2
Mixture Problems
(part 2)
Types
1. Find the concentration of a mixture.2. Find the amount required to create a given mixture.3. Find the concentration required to create a given mixture.4. Find two amounts required to create a certain mixture.
Bucket Method
amount
type
Miguel wants to make 20 L of a 47% saline solution by mixing together a 75% saline solution and a 5% saline solution. How much of each solution must he use?
Example:
Example:
amount
type
x
75%
20 – x
5% 47%
Write the equation: (multiply)
20 L
(x)(75) + (20 – x)(5) = (20)(47)
Example:
(x)(75) + (20 – x)(5) = (20)(47)
75x + 100 = 940
-100 -100
70x = 840
€
47×20
– 5x
70x + 100 = 940
Example:
70x = 840
x = 12
70 70
20 – x = 8
12L of 75%, 8 L of 5%
A metallurgist needs to make 7 kg of an alloy containing 32% platinum. He is going to melt and combine one metal that is 77% platinum with another metal that is 14% platinum. How much of each should he use?
Example:
Example:
amount
type
x
77%
7 – x
14% 32%
Write the equation: (multiply)
7 kg
(x)(77) + (7 – x)(14) = (7)(32)
Example:
(x)(77) + (7 – x)(14) = (7)(32)
77x + 98 = 224
-98 -98
63x = 126
– 14x
63x + 98 = 224
Example:
63x = 126
x = 2
63 63
7 – x = 5
2kg of 77%, 5kg of 14%
5 ml of an 32% acid solution was mixed with 11 ml of pure water. Find the concentration of the new mixture.
Example:
Example:
amount
type
5 ml
32%
11 ml
0% x
Write the equation: (multiply)
16 ml
(5)(32) + (11)(0) = (16)(x)
Example:
(5)(32) + (11)(0) = (16)(x)
160 + 0 = 16x160 = 16x
x = 10 16 16
10%
How many pounds of a metal containing 60% platinum must be combined with 12 lb of pure platinum to form an alloy containing 90% platinum?
Example:
Example:
amount
type
x
60%
12 lb
100% 90%
Write the equation: (multiply)
x + 12
(x)(60) + (12)(100) = (x + 12)(90)
Example:
(x)(60) + (12)(100) = (x + 12)(90)
60x + 1200 = 90x-1200 -120060x = 90x – 120
+ 1080
Example:
60x = 90x – 120 -90x -90x -30x = -120-30 -30
x = 4 4 lbs
How many quarts of an 80% acid solution must be mixed with 4 qt of a 50% acid solution to make a 60% solution?
Example:
Example:
amount
type
x
80%
4 qt
50% 60%
Write the equation: (multiply)
x + 4
(x)(80) + (4)(50) = (x + 4)(60)
Example:
(x)(80) + (4)(50) = (x + 4)(60)
80x + 200 = 60x-200 -20080x = 60x + 40
+ 240
Example:
80x = 60x + 40 -60x -60x 20x = 4020 20
x = 2 2 qt
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