# Algebra Mixture

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We know Algebra mixture problems are problems which find a final solution by adding or subtracting of two or more results of the same problem. We have some steps to derive the solution.

Step 1: from the problem, we can write an expression for some variables.

Step 2: If we have two equations, from that we need find the solution, by adding or by subtracting of equations.

Example 1:If the angles A and B are complementary angles. The angle A is 21 more than twice the other angles B. Find the angles A and B.

Solution: The given angles are A and B.

We know complementary means 90
°

From this we can write, A + B = 90………………………… (1)

From the problem we can write A = 2B + 21

Means A – 2B = 21…………………………………….. (2)

From (1) and (2), we can write (1) – (2)

A + B = 90

A – 2B = 21
-        +       -
3 B = 69

Divide this by 3, then we have B = 23.

From problem (1), A + B = 90

A + 23 = 90

A = 67

The final answer is A = 67 and B = 23.

Example 2: Robert and Peter started a business. In that business Robert invested \$5000 and Peter invested \$3000.Find the ratio of their shares.

Solution:  Robert’s share amount = \$5000

Peter’s share amount = \$3000

The ratio of their shares = 5000: 3000

= 5: 3.

Hence the ratio of their shares is 5:3