# Algebra 1 Problems

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Algebra 1 includes the following topics given below:
·         H.C.F. and L.C.M.

·        Simultaneous equation
·        Ratio, proportion and variation
·        Inequation
·        Graphs
·        Algebraic expressions
·        Polynomials
·        Surds
·        Exponents
·        Matrices
·        Fractions and decimals etc.

Examples of algebra 1 problems

From simultaneous equation: -

Example 1: - Sum of the ages of father and his son is 55 years. After 16 years father’s age becomes double that of his son. What are their present ages?

Solution: -Let the ages of the father and his son be x years and y years respectively.
Then from the first condition, we have
X + y = 55      … (1)
Again from the second condition of the problem, we have,
X + 16 = 2 (y + 16)
X – 2 y = 6     … (2)
Solving (1) and (2), we have x = 42 and y = 13.
Therefore the ages of the father and the son are 42 years and 13 years respectively.

From H.C.F.  and L.C.M.

Example 2: - The L.C.M. of two numbers is 2 x y times their H.C.F. If one number and the H.C.F. are respectively 10 x^3 y^2 and 5 x^2 y^2, then whatr is the other number?

Solution: - From the given information:
H.C.F. = 5 x^2 y^2 and
L.C.M. = 2 x y times of 5 x^2 y^2 =10 x^3 y^3

2nd number = (H.C.F. * L.C.M.) / 1st number
= (10 x^3 y^2 * 5 x^2 y^2) / 10 x^3 y^2
= 5 x^2 y^3