1. Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $30 one time activation fee and charges 8 cents a minute. The second plan has no activation fee and charges 13 cents a minute. After how many minutes of long distance calls will the cost of the two plans be equal in minutes?
2. Austin rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 72 cents for each mile driven. Austin had to pay $203.31 when he returned the truck. For how many miles did he drive the truck?
3. Jane will rent a fullsize car for a day. The rental company offers two different pricing options. Option A and option B. For each pricing option, cost (in dollars) is a function of miles driven. A= $110, B= $95 and 325 miles
If Jane drives 50 miles with the rental car, which option costs more? A or B?
How much more does it cost than the other option?
4. In a family there are two cars. The sum of the average miles per gallon obtained by the two cars in a particular week is 55. The first car has consumed 35 gallons during the week, and the second has consumed 40 gallons, for a total of 2075 miles driven by the two cars combined. What was the average gas mileage obtained by each of the two cars in that week?
5. A cyclist travels 90 km in 6 hours going against the wind and 75 km in 3 hours with the wind. What is the rate of the cyclist in still air and what is the rate of the wind?
6. The sugar sweet company is going to transport its sugar to market. It will cost $3500 to rent trucks, and it will cost an additional $125 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S, and then graph the equation.
1. Answer: 600 minutes
Suppose after x minutes of long distance calls the cost of the two plans are equal. Then we have
30 + 0.08x = 0.13x
Then we get 0.05x = 30, then x = 600 minutes.
2. Answer: 256 miles
Suppose Austin drove the truck for x miles, then we have
18.99 + 0.72x = 203.31
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