I need to rent a car for my upcoming trip. Rent-A-Gem charges $20.25 per day plus 14 cents per mile. Super Saver Rentals charges $18.25 per day plus 22 cents per mile. At first glance it looks as if I should go with Super Saver Rentals. Still, I'm concerned about the per-mile charge because I plan to do a lot of driving during all three days of my trip. How many miles would I have to drive to make the cost of renting a car from Rent-A-Gem the same as the cost of renting a car from Super Saver Rentals? Please read the problem carefully. Be sure that you give all the details of your solution process, including all the comparisons that you make in order to determine the answer.
Train A, traveling 70 miles per hour (mph), leaves Westford heading toward Eastford, 260 miles away. At the same time. Train B, traveling 60 mph, leaves Eastford heading toward Westford. When do the two trains meet? How far from each city do they meet?
To solve this problem, you'll need to know/use the distance formula: Distance = Rate x Time
Melanie is shopping for work clothes. She has found a dress for $75 and a two-piece suit for only $60. She does not have enough money for both, so she must choose only one. Of course, both are "dry clean only." If her dry cleaner charges $4.50 for a dress or $3 for each piece of a suit, which will be a better deal in the long run? How many times will she have to dry clean the purchased item before it is the better deal? Show how you arrived at your answer.
Your parents have decided to let you have your own phone line. They will pay the set-up fees, but you will have to pay your own bill. The telephone company gives you a choice of three plans.
Consider the following steps to determine which plan will be the better value:
1. For plans A, B and C, write equations that represent the total monthly phone bill in terms of the basic rate plus the number of phone calls. You might consider drawing an accurate graph as well.
2. Determine under what circumstances each plan would be best. Be specific about the number of phone calls where each plan would be preferable.
3. For a short answer, just state the number of calls where Plan A becomes less expensive than Plan B.)
A cereal bar is made from many ingredients including oats and chocolate. One unit of each ingredient provides units of protein and fat as shown in the table below, while the other ingredients have insignificant amounts of protein and fat. Is it possible to make a cereal bar that contains 7 units of protein and only 3 units of fat? If so, how many units of each ingredient should be used to make the cereal bar? If not, give an example of a cereal bar that is possible to make that has more units of protein than units of fat.
Hansel has goldfish that quadruple, or become four times as many, every month. Gretel has goldfish that increase by 20 every month. Right now, Hansel has 4 goldfish and Gretel has 128 goldfish. In how many months will they have the same number of goldfish? Show algebraically how you arrive at the answer.
Judy enters $3000 into a savings account and decides to put $125 in the account each month after that. The account earns 2.6% interest each year. Five years later, her younger sister Sally places $5000 into a savings account and puts $150 in the account each month after that. Her account earns 4.6% interest each year. How many years will it take until Sally has as much money in her account as Judy does in hers? Assume the interest rates remain constant.
What happens to the x-intercept of y = ax+b when you reverse the leading coefficient, a, and the constant, b? What happens to the x-intercept(s) of y= ax2 +bx +c when you reverse the leading coefficient, a, and the constant, c? What happens to the x-intercepts of a polynomial in the form y = axn+ bxn-1 +cxn-2+...+z when you reverse the leading coefficient, a, and the constant, z?