Chapter 3

Sarah wants to arrive at her friend's wedding at 3:00. The distance from Sarah's house to the wedding is 95 miles. Based on usual traffic patterns, Sarah predicts she can drive the first 15 miles at 60 miles per hour, the next 10 miles at 30 miles per hour, and the remainder of the drive at 70 miles per hour. (a) How long will it take Sarah to drive the first 15 miles? (b) How long will it take Sarah to drive the next 10 miles? (c) How long will it take Sarah to drive the rest of the trip? (d) What time should Sarah leave her house?

When solving a uniform motion problem, how does drawing a diagram of the situation help you?

In the following exercises, solve. Mona is planning her son's birthday party and has a budget of \(\$ 285\). The Fun Zone charges \(\$ 19\) per child. How many children can she have at the party and stay within her budget?

In the following exercises, solve. Carlos is looking at apartments with three of his friends. They want the monthly rent to be no more than \(\$ 2360\). If the roommates split the rent evenly among the four of them what is the maximum rent each will pay?

In the following exercises, solve. A water taxi has a maximum load of 1,800 pounds. If the average weight of one person is 150 pounds, how many people can safely ride in the water taxi?

In the following exercises, solve. Marcela is registering for her college classes, which cost \(\$ 105\) per unit. How many units can she take to have a maximum cost of \(\$ 1,365 ?\)

In the following exercises, solve. Arleen got a \(\$ 20\) gift card for the coffee shop. Her favorite iced drink costs \(\$ 3.79 .\) What is the maximum number of drinks she can buy with the gift card?

In the following exercises, solve. Teegan likes to play golf. He has budgeted \(\$ 60\) next month for the driving range. It costs him \(\$ 10.55\) for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?

In the following exercises, solve. Joni sells kitchen aprons online for \(\$ 32.50\) each. How many aprons must she sell next month if she wants to earn at least \(\$ 1,000 ?\)

In the following exercises, solve. Ryan charges his neighbors \(\$ 17.50\) to wash their car. How many cars must he wash next summer if his goal is to earn at least \(\$ 1,500 ?\)

In the following exercises, solve. Keshad gets paid \(\$ 2,400\) per month plus \(6 \%\) of his sales. His brother earns \(\$ 3,300\) per month. For what amount of total sales will Keshad's monthly pay be higher than his brother's monthly pay?

In the following exercises, solve. Kimuyen needs to earn \(\$ 4,150\) per month in order to pay all her expenses. Her job pays her \(\$ 3,475\) per month plus \(4 \%\) of her total sales. What is the minimum Kimuyen's total sales must be in order for her to pay all her expenses?

In the following exercises, solve. Andre has been offered an entry-level job. The company offered him \(\$ 48,000\) per year plus \(3.5 \%\) of his total sales. Andre knows that the average pay for this job is \(\$ 62,000\). What would Andre's total sales need to be for his pay to be at least as high as the average pay for this job?

In the following exercises, solve. Nataly is considering two job offers. The first job would pay her \(\$ 83,000\) per year. The second would pay her \(\$ 66,500\) plus \(15 \%\) of her total sales. What would her total sales need to be for her salary on the second offer be higher than the first?

In the following exercises, solve. Jake's water bill is \(\$ 24.80\) per month plus \(\$ 2.20\) per ccf (hundred cubic feet) of water. What is the maximum number of ccf Jake can use if he wants his bill to be no more than \(\$ 60\) ?

In the following exercises, solve. Marlon's TV plan costs \(\$ 49.99\) per month plus \(\$ 5.49\) per first-run movie. How many first-run movies can he watch if he wants to keep his monthly bill to be a maximum of \(\$ 100 ?\)

In the following exercises, solve. Kellen wants to rent a banquet room in a restaurant for her cousin's baby shower. The restaurant charges \(\$ 350\) for the banquet room plus \(\$ 32.50\) per person for lunch. How many people can Kellen have at the shower if she wants the maximum cost to be \(\$ 1,500 ?\)

In the following exercises, solve. Noe installs and configures software on home computers. He charges \(\$ 125\) per job. His monthly expenses are \(\$ 1,600\). How many jobs must he work in order to make a profit of at least \(\$ 2,400 ?\)

In the following exercises, solve. Katherine is a personal chef. She charges \(\$ 115\) per four-person meal. Her monthly expenses are \(\$ 3,150\). How many four-person meals must she sell in order to make a profit of at least \(\$ 1,900 ?\)

In the following exercises, solve. Melissa makes necklaces and sells them online. She charges \(\$ 88\) per necklace. Her monthly expenses are \(\$ 3745 .\) How many necklaces must she sell if she wants to make a profit of at least \(\$ 1,650 ?\)

In the following exercises, solve. Five student government officers want to go to the state convention. It will cost them \(\$ 110\) for registration, \(\quad \$ 375\) for transportation and food, and \(\$ 42\) per person for the hotel. There is \(\$ 450\) budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge \(\$ 5\) per car, how many cars must they wash in order to have enough money to pay for the trip?

In the following exercises, solve. Cesar is planning a 4-day trip to visit his friend at a college in another state. It will cost him \(\$ 198\) for airfare, \(\$ 56\) for local transportation, and \(\$ 45\) per day for food. He has \(\$ 189\) in savings and can earn \(\$ 35\) for each lawn he mows. How many lawns must he mow to have enough money to pay for the trip?

In the following exercises, solve. Alonzo works as a car detailer. He charges \(\$ 175\) per car. He is planning to move out of his parents' house and rent his first apartment. He will need to pay \(\$ 120\) for application fees, \(\$ 950\) for security deposit, and first and last months' rent at \(\$ 1,140\) per month. He has \(\$ 1,810\) in savings. How many cars must he detail to have enough money to rent the apartment?

Maximum Load on a Stage In 2014 , a high school stage collapsed in Fullerton, California, when 250 students got on stage for the finale of a musical production. Two dozen students were injured. The stage could support a maximum of 12,750 pounds. If the average weight of a student is assumed to be 140 pounds, what is the maximum number of students who could safely be on the stage?

Maximum Weight on a Boat In \(2004,\) a water taxi sank in Baltimore harbor and five people drowned. The water taxi had a maximum capacity of 3,500 pounds (25 people with average weight 140 pounds). The average weight of the 25 people on the water taxi when it sank was 168 pounds per person. What should the maximum number of people of this weight have been?

Wedding Budget Adele and Walter found the perfect venue for their wedding reception. The cost is \(\$ 9,850\) for up to 100 guests, plus \(\$ 38\) for each additional guest. How many guests can attend if Adele and Walter want the total cost to be no more than \(\$ 12,500 ?\)

Shower Budget Penny is planning a baby shower for her daughter-in-law. The restaurant charges \(\$ 950\) for up to 25 guests, plus \(\$ 31.95\) for each additional guest. How many guests can attend if Penny wants the total cost to be no more than \(\$ 1,500 ?\)

Find your last month's phone bill and the hourly salary you are paid at your job. (If you do not have a job, use the hourly salary you would realistically be paid if you had a job.) Calculate the number of hours of work it would take you to earn at least enough money to pay your phone bill by writing an appropriate inequality and then solving it.