Algebra II - Chapter 8 Review Determine the least common denominator (LCD) of the rational expressions 1 2 Add, subtract, multiply, or divide as indicated List any restrictions for the variable(s) and simplify the answers when possible 3 4 5 6 Solve each equation List any restrictions and check your answer 7 8 9 10 Les has 200 cubic yards of topsoil that contains 10% rocks A customer will buy all of Les s topsoil if it contains no more than 6% rocks So Les will add some topsoil that is 4% rocks so that the mixture is 6% rocks Write and solve and equation to calculate how much Les must add
11 12 Abby and Charlie are roommates Abby can clean their apartment in 3 hours Charlie can do it in 5 hours If they work together, how long will it take Abby and Charlie to clean their apartment? 13 Ricky paddles his canoe at a rate of 6 miles per hour in still water Last weekend he canoed on Carver Creek going downstream with the current for 9 miles and then returning upstream against the current If the trip took him 4 hours to complete, what was the speed of the current? 14 Trey buys a 500 ml bottle of rubbing alcohol The bottle contains a solution of 70% alcohol and 30% water The instructions for his toy train set say he should use a solution of 40% alcohol and 60% water to clean the tracks Write and solve an equation to determine how much water Trey must add to the solution he purchased to have the correct solution for cleaning the tracks 15 Matthew is an aerial photographer He photographs a 200-mile long oil pipeline that runs straight from east to west He flies the 200 miles from west to east with an eastward tailwind He returns over the same route and flies 200 miles against an eastward headwind The total time of the 400-mile flight is 180 minutes The plane travels at a speed of 150 miles per hour without a tailwind or headwind Assume the wind speed is constant during the entire flight Write and solve an equation to determine the wind speed during Matthew s flight 16 Ramona is trying to decide between 2 satellite Internet providers ProSat Internet charges a $250 installation fee and a monthly fee of $50 SuperSat Internet charges a $90 installation fee and a monthly fee of $58 Write and solve an equation to determine when the average monthly cost (including installation and monthly fees) of each service would be the same Show your work
Algebra II - Chapter 8 Review Answer Section 1 2 3 4 5 6 7 8 9 10 11 12 between 1 and 2 hours
13 The speed of the current was 3 miles per hour Let r represent the speed of the current 14 Trey must add 375 ml of water to the original solution in order to obtain a solution of 40% alcohol and 60% water Let x represent the amount of water added to the original solution The original solution contains 350 ml of alcohol or 15 The wind speed during Matthew s flight was 50 miles per hour Let x represent the wind speed in miles per hour Matt made the west to east flight in hours He made the east to west flight in hours The total flight time was 180 minutes or 3 hours
16 The average monthly cost of each service will be the same in 20 months Let x represent the number of months of Internet service The average monthly cost of ProSat Internet is dollars The average monthly cost of SuperSat Internet is dollars