Bus Tour (Ratios)

Story A: Double Decker City Tours' buses have 36 seats. For safety and profit, they always need to know exactly who is on the bus. They can't afford to have too many riders with a discount on the bus. At the first stop, ⅓ of the seats are empty, and the ratio of adults to students is 3:1. Who is on the bus? At the second stop, 6 people get on the bus, and the ratio of adults to students is now 2:1. How many of each are on the bus? At the third stop, some people get off, and some get on the bus. There are 12 fewer people on the bus when it leaves stop 3. The ratio of adults to students is now 4:5. How many of each are on the bus now? After the fourth stop, 7 people get on the bus. The ratio of adults to students is 2:3. How many adults and students are on the bus? At the last stop, ⅕ of the people on the bus get off. The ratio of adults to students is now 1:1. How many adults and students are on the bus at the last stop?

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Bus Tour (Ratios)

Story B: Double Decker City Tours' buses have 48 seats. For safety and profit, they always need to know exactly who is on the bus. They can't afford to have too many riders with a discount on the bus. At the first stop, ¾ of the seats are filled, and the ratio of adults to students to tourists is 1:5:3. Who is on the bus? At the second stop, 12 people get on the bus and 6 get off. The ratio of adults to students to tourists is now 1:2:3. How many of each are on the bus? At the third stop, some people get off, and some get on the bus. There are 10 fewer people on the bus when it leaves stop 3. The ratio of adults to students to tourists is now 2:1:5. How many of each are on the bus now? After the fourth stop, 16 people get on the bus. The ratio of adults to students to tourists is now 3:2:7. How many adults, students, and tourists are on the bus? At the last stop, 26 of the people on the bus get off, and 8 get on. The ratio of adults to students to tourists is now 4:1:1. How many adults, students, and tourists are on the bus at the last stop?

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Deer Population (Ratios)

Donut Box (Ratios)

James is responsible for getting the donuts for the staff meeting this morning. He knows he needs one box with 24 donuts, chocolate and glazed in a 1:3 ratio, and another box with 36 donuts, glazed, cinnamon, and chocolate in a ratio of 2:3:4. When Alberto walks in for the meeting, he realizes some donuts are already gone. Which ones have been taken?

Needed Information: The ratio of cinnamon to chocolate to glazed donuts is now 3:5:6.

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Penny Tower (Proportional Thinking)

With a few pennies and a ruler, can you answer this question? How tall would a tower of one million pennies be? 

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Bracelets (Unit Rate with Length and Prices)

Li, the president of her school's ASB, is tasked with making and selling 500 bracelets for a school fundraiser. String is $7 for 3 rolls per pack (each roll has 32 ft). The beads are $12 for 2 bags per pack (each bag has 1000 beads). Each bracelet uses 12 inches of string and 24 beads. What is the total cost and the cost of each bracelet?

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Cat Food (Unit Rate with Prices)

Commute (Unit Rate with Speed)

Alberto, Sara, and Andrew take the train from Amsterdam to Paris. Alberto takes the slower train, which travels 120 km/h, and does not stop in Antwerp. Sara and James take the faster train, which travels 150 km/h, but stops in Antwerp. It takes the faster train 40 minutes to get to Antwerp from Amsterdam and will stop there for 30 minutes. Once it continues after the stop in Antwerp, does Sara and Andrew’s train catch Alberto’s train? When?

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Dakar Rally (Unit Rate with Speed)

Welcome to the Dakar Rally, the world's most famous and most challenging rally race, racing across undeveloped terrains such as mountain passes and deserts. Driving hundreds of km a day, drivers and their vehicles are pushed to the limit. The rally tests their technique, mental and physical strength, mechanical skill, and experience to cover nearly 9,000 km in two weeks. More than half of the vehicles that begin the race fail to finish it, epitomizing the toughness of the rally. Stage 9 of this year's Dakar Rally covers a distance of 831 kilometers. Let's look at the virtual map to see the location of the teams in the race and their speeds. How long will it take each team to get to the finish?

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Distance Run (Unit Rate with Speed)

Today is marathon day at the local gym, a 12.5-mile run on a treadmill. Sara, Li, and Nia want to get on the leaderboard, so they set the treadmill at a steady pace and go for it. Based on their current pace, where will they rank on the leaderboard?

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Fastest (Unit Rate with Speed)

Li, James, and Alberto are on their way to tour London Stadium, the stadium in London that was used for track during the 2012 Olympics and is now home to West Ham United. Many references to the Olympics remain outside the stadium, including the track world records on a plaque next to one of the entrances.  Who ran the fastest?

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Fruit Stand (Unit Rate with Prices)

Alberto is going to the market to buy apples, bananas, and oranges at a fruit stand with 15 dollars in cash. He buys five pounds of bananas, four pounds of apples, and three pounds of oranges. Bananas are 80¢ per pound, apples are $1.40 per pound, and oranges are $1.25 per pound. How much change does he receive?

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Groceries (Unit Rate with Prices)

We all need groceries, but some of us go about it a little differently. Li and James are on a budget and want the cheapest option for the items they need. Which ones are the better deal?

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Interview (Unit Rate with Distance and Time)

Nia has an interview that starts in 2 hours and is 160 miles from her current location. Will she make it in time if she drives the speed limit? If so, how much time does she have left over? If not, how fast will she need to drive to make it? After 30 minutes of speeding to make the interview, traffic is stopped for 10 minutes to clear an accident. Because of this, Nia has to drive even faster to make it on time. How much faster?

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Paint Store (Unit Rate with Prices)

Sara needs to buy 20 gallons of paint. She has two choices. Erwin-William sells 12 gallons for $186.60. Bun-Edward sells 5 gallons for $74.65. How much will Sara save if she buys 20 gallons of paint at Bun-Edward?

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Trail Run (Unit Rate with Distance and Time)

Alberto goes on a jog through the forest five days a week. Every day he takes a new trail and keeps track of his distance and time on his watch. When he comes home, he records his distance and start and finish time. What is Alberto’s mile time for each of his runs?

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Trainer (Unit Rate with Prices)

Andrew works as a personal trainer. He has the option to be paid per client, at $75 per client, or to work by the hour, at $40 per hour. He would be able to see four clients each day or work 7 hours a day. How much more would he make in a 5-day work week if he chose the right option? After six months, Andrew has established a reputation as a top personal trainer. He now sees 25 clients during the week and charges $85. How many hours will he need to work during the week if they can give him a $10 raise, so that he earns the same as being paid per client? 

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Water Leak (Unit Rate with Measurements)

Andrew and James have a leak under the sink, so they place a 1-gallon bucket under it while they wait for the plumber. They placed the bucket under the leak at 9 a.m. When they returned to check on it, they found 30 fluid ounces of water in the bucket. If they don't empty the bucket now, what time do they need to return to empty it so it doesn't overflow?

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Leaky Faucet (Unit Rates and Unit Conversion)

Sara and James are at their vacation home in the woods when Sara notices the hose bib on the side of the house is leaking water. The calcium buildup prevents the hose bib from completely closing. They could try to clean it or replace it. Sara wants to know how much water leaks out of this hose bib. James gets a stopwatch and measuring spoons and finds out 1 tsp leaks out of the hose bib every 6 minutes. How much water is that in a week, a month, a year?

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