Algebra 1 Problems

Algebra 1 Problems Algebra 1 includes the following topics given below: H.C.F. and L.C.M. Simultaneous equation Quadratic equation Ratio, proportion and variation Inequation Quadratic surds 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 fathers 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