STATION #1: VARIABLES ON BOTH SIDES (BASIC) Copy and solve each equation. Show all work. 1. 18 6x = 2x + 6 x = 3 2. z = 84 6z z = 12 3. 3 f = 6f + 24 f = 3 4. 3(2 + m) = 2(3 m) m = 0 5. 4(2y 1) + 5 = 3y + 1 y = 0 1. Solve the equation: 1 h + 1 (h 6) = 5 h + 2 No solution exists 2 3 6 2. A coffee shop offers a special: 33% extra free or 33% off the regular price. Which offer is a better deal? Explain your reasoning. 33% off the regular price
STATION #2: VARIABLES ON BOTH SIDES (ADVANCED) Copy and solve each equation. Show all work. 1. 4b + 4(1 b) = b 9 b = 13 2. 3(x 1) + 8(x 3) = 6x + 7 5x x = 7 Follow the instructions for a number puzzle: Take the number formed by the first 3 digits of your phone number and multiply it by 40 Add 1 to the result Multiply by 500 Add the number formed by the last 4 digits of your phone number, and then add it again Subtract 500 Multiply by 12 1. What is the final number? 2. How does this number puzzle work? 3. Can you invent a new number puzzle that gives a surprising result?
STATION #3: FRACTION EQUATIONS Copy and solve each equation. Show all work. 1. 3x = 15 8 x = 5 8 2. a + 1 3 = 3 4 x = 5 12 3. 64 = 1 x x = 512 8 4. 2x = 8 9 x = 4 9 5. 0.25z = 4 z = 16 1. Jada s neighbor said, My age is the difference between twice my age in 4 years and twice my age 4 years ago. How old is Jada s neighbor? 16 2. Another neighbor said, My age is the difference between twice my age in 5 years and and twice my age 5 years ago. How old is this neighbor? 20 3. A third neighbor had the same claim for 17 years from now and 17 years ago, and a fourth for 21 years. Determine those neighbors ages. 68 and 84
STATION #4: EQUATION WORD PROBLEMS (PART 1) Label variables and create and solve equations for each problem. Do not copy the problems. 1. Sally has practiced law three years longer than her younger brother. Together, they have a total of 21 years of practice. How long has her brother practiced law? x = years brother has practiced law x + x + 3 = 21 x = 9 years 2. Juan and Ingrid went selling magazine subscriptions. Ingrid sold four fewer subscriptions than twice as many as Juan sold. Together, they solve 23 subscriptions. How many subscriptions did each sell? x = number of magazine subscriptions sold by Juan x + 2x 4 = 23 x = 9 Juan sold 9 subscriptions. Ingrid sold 14 subscriptions 3. A college student is moving into a campus dormitory. The student rents a moving truck for $19.95 plus $0.99 per mile. Before returning the truck, the student fills the tank with gasoline, which costs $65.32. The total cost is $144.67. How many miles did the student drive the truck? x = miles driven in the truck 19.95 + 0.99x + 65.32 = 144.67 x = 60 miles 1. Use the distributive property to create an equivalent expression that uses the fewest number of terms: ((((x + 1) 1 ) + 1) 1 ) + 1. If we wrote a new expression following the same pattern so that there 2 2 were 20 sets of parentheses, how could it be expanded into an equivalent expression that uses the fewest 1 1 number of terms? (x + 7) and (x + 4 2 10 211 1)
STATION #5: EQUATION WORD PROBLEMS (PART 2) Label variables and create and solve equations for each problem. Do not copy the problems. 1. A car-rental company charges $22 to customers for the first mile plus an additional $0.75 for every additional mile you drive. If a customer paid $63.75 after using a car for a day, how many miles did they drive? m = miles driven 22 + 0.75m = 63.75 m = 55 2 3 They drove 56 2 miles that day 3 2. Steve pays $75 in art supplies and plans on selling paintings he has made. If he sells each painting for $15 and wants to make a profit of $405, how many paintings must he sell? p = cost of a single painting 15p 75 = 405 p = 32 paintings 3. Victor spent $20.60 at the carnival. He paid $8 at the entrance and 45 cents for each ride he went on. How many rides did he go on? r = number of rides he went on 8 + 0.45r = 20.60 r = 28 rides 1. What is the smallest number that has a remainder of 1, 2, and 3 when divided by 2, 3, and 4, respectively? Are there more numbers that have this property? 11; yes
STATION #6: EQUATION PERIMETER PROBLEMS Label variables and create and solve equations for each problem. Do not copy the problems. 1. The perimeter of a triangular trail is 20 km. The first trail is 1 km shorter than twice the length of the second trail. The third trail is 2 km longer than the first. Find the length of each trail. x = length of second trail 2x 1 + x + 2x 1 + 2 = 20 x = 4 First trail: 7 km Second trail = 4 km Third trail = 9 km 2. The perimeter of a rectangular lot is 260 m. The length exceeds the width by 20 m. Find the dimensions of the lot. x = width of rectangular lot x + 20 + x + 20 + x + x = 260 x = 55 width = 55 m length = 75 m 3. The side of a square is twice as long as the side of an equilateral triangle. The perimeter of the square is 60 cm more than the perimeter of the triangle. What are the lengths of the sides of the square and the triangle? x = side of the equilateral triangle 2x + 2x + 2x + 2x = 60 + x + x + x x = 12 Side of equilateral triangle = 12 cm Side of square = 24 cm 1. Han, his sister, his dad, and his grandmother step onto a crowded bus with only 3 open seats for a 42- minute ride. They decide Han s grandmother should sit for the entire ride. Han, his sister, and his dad take turns sitting in the remaining two seats, and Han s dad sits 1.5 times as long as both Han and his sister. How many minutes did each one spend sitting? Grandmother: 42, Dad: 36, Han: 24, Sister: 24
STATION #7: EQUATION DIAGRAMS Create a diagram for each situation. Then create an equation and solve, showing all work. 1. Andre wants to save $40 to buy a gift for his dad. Andre s neighbor will pay him weekly to mow the lawn, but Andre always gives a $2 donation to the food bank in weeks when he earns money. Andre calculates that it will take him 5 weeks to earn the money for his dad s gift. Draw a diagram to represent the situation and find how much Andre s neighbor pays him each week to mow the lawn. X 2 X 2 X 2 X 2 X - 2 Total of boxes = 40 5(x 2) = 40 x = $10 each week to mow the lawn 2. A family buys 6 tickets to a show. They also each spend $3 on a snack. They spend $24 in total. How much did each ticket cost? X + 3 X + 3 X + 3 X + 3 X + 3 X + 3 Total of boxes = 24 6(x + 3) = 24 x = $1 3. A piece of scenery for the school play is in the shape of a 5-foot-long rectangle. The designer decides to increase the length. There will be 3 identical rectangles with a total length of 17 feet. By how much did the designer increase the length of each rectangle? X + 5 X + 5 X + 5 Total of boxes = 17 3(x + 5) = 17 x = 2 3 feet 1. In the diagram, 9 toothpicks are used to make three equilateral triangles. Figure out a way to move only 3 of the toothpicks so that the diagram has exactly 5 equilateral triangles.
STATION # 8: Proportions Review Solve each problem. Show all work. Do not copy the problem. 1. A recipe for sparkling grape juice calls for 1 1 quarts of sparkling water and 3 quart of grape juice. 2 4 a. How much sparkling water would you need to mix with 9 quarts of grape juice? 18 quarts b. How much grape juice would you need to mix with 154 quarts of sparkling water? 15/8 quarts 2. To make a shade of paint called jasper green, mix 4 quarts of green paint with 2 cups of black paint. 3 How much green paint should be mixed with 4 cups of black paint to make jasper green? 24 quartsw 3. An airplane is flying from New York City to Los Angeles. The distance it travels in miles, d, is related to the time in seconds, t, by the equation d = 0.15t. a. How fast is it flying? Be sure to include the units. 0.15 miles per second b. How far will it travel in 30 seconds? 4.5 miles in 30 seconds c. How long will it take to go 12.75 miles? 85 seconds 1. At step 2: 33.3% At step 3: 77.8% At step 10: 1,675.8%