Pre-Algebra and Algebra:
There are 4 red marbles, 2 blue marbles, 1 yellow marble, and 3 green marbles.
1. What is the probability that you will choose a red marble first, replace the marble, and then choose a blue marble?
2. What is the probability that you will choose a red marble first, keep the marble, and then choose a blue marble?
3. P(red, red, red) without replacing.
1. Plumber problem. Bathroom water is all plugged up and you need to hire a plumber. Company A charges $20 up front and $10 per hour and Company B charges nothing up front but $15 per hour. Which company would be better to hire? When would it not matter?
2. One day a shoe company bought 10 adult shoes and 20 children shoes for $600. The next week they bought 15 of each costing $750. How much does each pair of shoes cost?
1. Susie receives a gift card worth $25 to purchase online music and games. Each song costs $0.89 and each game costs $1.99. She wants to buy at least 15 items with this card. How many songs and games can she purchase? Set up a system of inequalities that represents this scenario, graph and then come up with a couple solutions.
2. The length of a rectangle is 8 cm more than twice the width. The perimeter of the rectangle is 40 cm. Find the dimensions of the rectangle using systems.
1. A boat is rowed 10 miles downstream in 2 hours, and then rowed the same distance upstream in 3 1/3 hours. Find the rate of the boat in still water and the rate of the current.
2. With the wind, an airplane travels 2200 miles in 4 hours. Against the wind, it takes 5 hours to travel 2350. Find the rate of the wind and the rate of the plane in still air.
1. John flies from Atlanta, Georgia, to San Francisco, CA. It takes 5.6 hours to travel 2100 miles against the head wind. At the same time Debby flies from San Francisco to Atlanta. Her plane travels with the same average airspeed but, with a tail wind, her flight takes only 4.8 hours. Using Systems, find the airplane and wind speeds.
2. Several students decide to start a T-shirt company. After initial expenses of $280, they purchase each T-shirt wholesale for $3.99. They sell each T-shirt for $10.99. How many must they sell to break even?
1. A piece of glass with an initial temperature of 99˚ C is cooled at a rate of 3.5 degrees Celsius per minute (˚C/min). At the same time, a piece of copper with an initial temperature of 0˚ C is heated at a rate of 2.5˚ C/min. Let m = the number of minutes, and t = the temperature in degrees Celsius after m minutes.
a. Write a system of equations that relates the temperature t of each material to the time m. Solve the system.
b. Writing Explain what the solution means in this situation.
Solve and graph the following:
1. - 3x + 6 - 5x > 22 2. 15x + 10 ≥ 8x - 4 3. 7x - 9 -5x = 11
The computer stopped while doing the Wiley's Restaurant's time sheets. There was no record of exactly how long each person worked. The computer did say that Lisa and Myles together worked 60 hours, Nick and Lisa together worked 70 hours, and Myles and Nick together worked 50 hours. They each are to be paid $8 per hour. How much should each person be paid?
The second angle of triangle is 50 degrees less than 4 times the first angle. The third angle is 40 degrees less than the first. Find the measures of the three angels using systems of equations.
Suppose you want to combine two types of fruit drink to create 24 kilograms of a drink that will be 5% sugar by weight. Fruit drink A is 4% sugar by weight, and Fruit Drink B is 8% sugar by weight. Using Systems, find how much of each type of fruit drink you need to use.
1. The measure of the angles of a triangle are given as 8x, (2x-4), and (4x +9). What are the measures of each angle?
2. In a certain triangle, the measure of one angle is 7 times the measure of the smallest angle, and the measure of the remaining angle is the sum of the measures of the other two angles. Determine the measure of each angle.
3. The second angle of triangle is 50 degrees less than 4 times the first angle. The third angle is 40 degrees less than the first. Find the measures of the three angles.
9/19: Need a plumber. The plumber charges $40 upfront and $60 per hour. You only have $400 to spend on the problem. How many hours could you pay the plumber?
Mrs. Carle found some cool earings at a farmer's market. They were $15 each. If she only has $85, how many can she buy?
6/4: Describe the following graphs without sketching:
y - 7 = 2(x + 2)
Write the equation 3x+2y = 5 in slope intercept form.
Write the equation y + 1 = 2(x - 2) in standard form.
6/5: An academic team is going to a state mathematics competition. There are 30 people going on the trip. There are 5 people who can drive and 2 types of vehicles, vans, and cars. A van seats 8 people, and a car seats 4 people, including drivers. How many vans and cars does the team need for the trip?
5/14: A cup is 6 cm tall, including a 1.1 cm lip. Find a function that represents the height of a stack of cups in terms of the number of cups in the stack. Find the height of 8 cups stacked.
Suppose you enlarge a photograph that is 4 in. wide and 6 in. long so that its dimensions are 20% larger than its original size. Write a rule for the length of the copies. What will be the length if you enlarge the photograph five times? (Hint: The common ratio is not just 0.2. You must add 20% to 100%.)