# Intermediate Algebra Problems With Answers - Sample 1

A set of intermediate algebra problems, with answers, are presented. The solutions are at the bottom of the page.

 For what value of the constant K does the equation 2x + K x = 3 have one solution?. For what value of the constant K does the equation K x2 + 2x = 1 have two real solutions? For what value of the constant K does the system of equations 2x - y = 4 and 6x - 3y = 3K have an infinite number of solutions? Find Y so that the points A(0 , 0), B(2 , 2) and C(-4 , Y) are the vertices of a right triangle with hypotenuse AC. Find M so that the lines with equations -2x + My = 5 and 4y + x = -9 are perpendicular. The length of a rectangular field is 7/5 its width. If the perimeter of the field is 240 meters, what are the length and width of the field? Peter wants to get $200,000 for his house. An agent charges 20% of the selling price for selling the house for Peter. a) What should be the selling price? b) What will be the agent's commission? John's annual salary after a raise of 15% is$45,000. What was his salary before the raise? It took Malcom 3.5 hours to drive from city A to city B. On his way back to city A, he increased his speed by 20 km per hour and it took him 3 hours. a) Find the average speed for the whole journey. Let R be a relation defined by R = {(4,3),(x 2,2),(1,6),(-4,0)}. a) Find all values of x so that R is not a function.