1 Proportions

1.1 Exercises

1.1.1 Problem set

For each of the following problems, identify also if the relationship between the independent and dependent quantities is a proportion.

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, 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?

1.1.3 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?

1.1.4 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?

1.1.5 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