1 Proportions

1.1 Exercises

1.1.1 Problem set

1. Say, you are doing a summer job. Your goal is to earn a certain amount of money so that you could buy a computer for yourself. What is a good independent quantity that the money you earn depends on?
2. A pediatrician wants to understand a child’s growth by checking the height of the kid over time. What is the independent quantity that the dependent quantity height relates to?
3. A family is planning a vacation to Orlando, and is estimating how much it costs them for hotel stay on the trip. What is a good independent quantity that the cost could be related to?
4. A paving company is estimating the time it would take to pave a street. What is a good independent quantity that time it takes to pave could be related to?
5. A city council is making certain plans for the city development based on how the population of the city grew over time in the past. What is a good independent quantity that population of the city could be related to?

1.1.2 Problem set

For each of the following problems, identify if the relationship is a proportion.

1. Cost of apples depending on the number of apples purchased
2. A kid’s height depending on the kid’s age
3. Weight of a stack of text books depending on the number of text books
4. Amount of time needed for math homework depending on the number of math problems in the homework
5. Weight of flour needed depending on the number of cookies to be baked
6. Distance travelled by a train at constant speed depending on time elapsed
7. Distance travelled by a car in a city depending on time elapsed
8. Cost of pizza depending on number of toppings of the pizza
9. Cost of a holiday trip depending on the number of days of the holiday

1.1.3 Problem set

For each of the following problems, determine the independent quantity based on the question asked. Then, explain the meaning of unit rate in the problem’s context and find the value of the unit rate.

1. men are able to paint square feet of walls in a day. How many men are required to paint square feet of walls in a day?
2. To pave a m long road in a day, it takes machines. How many machines does it take to pave a m long road in the same amount of time?
3. backpacks cost . How many backpacks could I buy with ?
4. During a hurricane relief, tonnes of grain were required to support an affected neighborhood with families. How many tonnes of grain are required to support a neighborhood of families?
5. high school students are able to arrange books in bookshelves in one hour. How many bookshelves can students arrange in one hour?
6. A landlord makes per year by renting out condo units.
   1. How much money will he make per year if he rents out condo units?
   2. If he needs to make at least per year, how many condos must he rent out?
7. A car drives miles on gallons of gas.
   1. How many miles can be driven on gallons of gas?
   2. How many gallons of gas are required to drive miles?

1.1.4 Problem set

1. high school students are able to arrange books in a library in hours. How many hours do students need to arrange the library books?
2. A service organization stores food in their pantry . It estimates if the pantry is full, the food in there is sufficient to feed people for days. At one particular time, the organization is required to house people. How many days would the food (from the pantry that is full) last feeding all the people?
3. It takes machines days to pave a road. How many machines are required to pave a similar road in days?
4. It takes days for painters to paint the interior of a house. How many days would it take for painters to paint the interior of a similar house?

1.1.5 Problem set

1. A car going at mph is able to cover a certain distance in minutes. How much time will a car going at mph take to cover twice that distance?
2. Sam runs at mph, while Jack runs at mph. They both are running along the same loop in a park. What is the proportion of time taken by Sam to the time taken by Jack?

1.1.6 Problem set

1. It takes machines days to pave a m long road. How many machines does it take to pave a m long road in days?
2. It takes men days to paint a sq. ft wall. How many sq.ft of the wall can men paint in days?
3. It takes men days to paint a sq. ft wall. How many days will it take men to paint sq. ft. wall?
4. It takes men days to plant seeds in a sq. ft. field. How many days does it take for men to plant seeds in a sq. ft. field?
5. Marvin can mow a yard in hours. If Marvin and Tim work together, they can finish the mow in hours. If Tim works by himself, how long would it take for Tim to mow the yard?

2 Linear relationships

2.1 Exercises

2.1.1 Problem set

1. A volunteer team plans to complete a long flowerbed along the side of a local park. A section of square feet of the flowerbed was already planted when the team got there. If the team is able to plant square feet every hour, give an equation that gives the total area of the flowerbed planted based on the time elapsed.
2. A new aquarium exhibit starts with gallons of water already sitting in the bottom of a large display tank. A pump is turned on to fill the rest of the tank, adding gallons every minute. Give an equation that gives the total volume of water in the tank based on the time elapsed since the pump was turned on.
3. A local bakery fulfills catering orders by charging per person served in addition to a fixed setup fee of . Give an equation that gives the total cost of catering based on the number of people served.
4. A hiker starts hiking down from a mountain shelter located at an elevation of 2,800 feet above sea level. If she hikes down feet every minute, write an equation that gives the hiker’s elevation based on the time elapsed since she started her descent.
5. A standard shipping box can hold a maximum weight of pounds. A worker puts heavy books into the box, where each book weighs pounds. Write an equation that gives the remaining weight capacity of the box based on the number of books placed in the box.
6. A driver starts a road trip with a full -gallon gas tank in her sedan. On the highway, her car consumes gallons of fuel every minute. Write an equation that gives the amount of fuel remaining in the gas tank based on the distance driven.

2.1.2 Problem set

In each of the following problems, explain the meaning, in the problem’s context, of each of the numbers seen in the equation.

1. A gardener transplants a young bamboo shoot into her yard. The height of the bamboo shoot after a certain number of days is given by .
2. The rental cost (in dollars) for an event space depending on number of hours the space is rented for is given by .
3. An online gamer starts streaming with an existing group of followers. The total number of followers on their channel depending on number of weeks of streaming is given by the equation .
4. A baker starts her morning with a fresh batch of chocolate chip cookies. The number of cookies remaining on display depending on number of hours elapsed is given by .
5. A customer signs up for a smartphone plan with a set monthly data limit. The amount of high-speed data (in gigabytes) remaining depending on the number of hours of streaming video is given by the equation .
6. A scuba diver begins their descent into the ocean from the water’s surface. The diver’s height (in feet) from depending on the number of minutes elapsed is given by the equation .