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Algebra Mixture Problems

TopAlgebra is the branch of mathematics concerned with the study of the rules of operations and Relations between variable and constants. In Algebra to represent the unknown quantity we let a variable which is a letter or symbol.
For a variable we can use any letter of the alphabet such as:
P + 3
Q – 7
And the group of Numbers, symbols, and variables that express an operation is called algebraic expression.

To evaluate the algebraic expression we simply combine like terms and combine all operations in the equation, like in the following equation:
P + 3 + p + 3 = 10
=> 2p + 6 = 10
=> 2p = 10 - 6
=> p = 4/2
=> p = 2

In Algebra Mixture Problems there are basically word problems where quantities of different values are mixed together. In such type of problems we generally use following terms:
Words that refer to addition are: - Sum, More than, Increased, Plus, Altogether, etc.
Words that refer to subtraction are: - Decreased, Less, Difference, minus, etc.
Such that:
Ten more than a number can be written as [n +10]
A number decrease by 5 i.e. [w -5]
A number increased by 8 i.e. [n + 8]
The sum of a number & 9 i.e. [n + 9]
4 more than a number i.e. [y + 4]
Now let us go through this algebra mixture problem we have a pharmacist having 30L of a 10% drug solution. Let us find out how many liters of 5% solution must be added to get a mixture that is 8%.

To solve mixture problems, we form two equations. Let ‘p’ be the unknown volume (in liters) of the 5% solution so 30+p is the volume of the total mixture which is 8% solution. The equations are
P + 30 = p + 30 ………………………………… (1)
0.05p + 0.10(30) = 0.08 (p +30) ………... (2)
Solving equation (2) we get,
P = 20
Therefore, 20 Liters of 5% must be added to 30L of 10% to get a mixture that is 8%.