Consider the numbers Fn defined by the following formula:
where n may be any positive integer. Calculate F1 through F5. Do you notice anything suprising?
Sequence Formula
Set 09
Money Giving
Anthony had twice as much money as Russell, but after Anthony gave $35 to Russell, Russell had 3 times as much money as Anthony. How much money did Russell have at the start?
Solar Panel
If an eco-lightbulb is sold for $x, there is a loss of 15% based on the cost of materials required to produce it. If the same bulb is sold for $y, there is a profit of 15% based on the cost. What is the ratio of x to y?
Daniel Boone, Plum Creek
Daniel Boone can paddle his canoe at 15 mph in still water. He is, however, paddling on Plum Creek, which rages along at 5 mph. He paddles downriver for a while, then turns around and paddles back upstream to his starting point. What is his average speed for the entire trip?
Formula for Necessary Return Speed
If Alice can make a trip of m miles in t hours, at what rate must she make the return trip, given that it is possible to do so, so that the average speed for the whole journey will be k miles per hour?
Pompeii Geothermal Corp. Wages
You work for the Pompeii Geothermal Corporation, based in the southern part of Ohio. Last year you got a 10% pay raise. But now times are tough, and you are going to have to go back to your old pay rate. As a matter of interest, by what percent are your wages being lowered to get you back to where you were before you got your raise?
Inequality with 2 Absolute Values
The set of real solutions of the inequality |x – 1| + |x + 2| < 5 is:
- -3 < x < 2
- -1 < x < 2
- -2 < x < 1
- -3/2 < x < 7/2
- empty (no solutions)
Timbuktu Post Office
When a careful count was taken a few years back, the Timbuktu Post Office handled at least 3120 letters and 1890 advertising brochures daily. The canceling machine then in use could handle 390 letters and 315 brochures per hour at an hourly cost of $2.10. The post office was planning to acquire a new and improved model which could handle 520 letters and 210 brochures per hour at a cost of $2.70 per hour. Neither machine could be run for more than 10 hours per day due to internal heating. Neither machine could handle more than the maximum per hour in either category. For example, if the current machine was canceling only brochures, it still couldn’t handle more than 315 brochures per hour, and it still couldn’t run more than 10 hours per day without melting down. With these constraints, what would be the most economical way to run the post office canceling operation if they purchased the new machine?
Product = TTT
In the following equation, each of the letters represents a uniquely different digit in base ten. Suppose:
(YE)(ME) = TTT, where the number YE is less than ME in the product on the left.
Then the sum E + M + T + Y equals:
- 19
- 20
- 21
- 22
- 24
Sheriff Election
Art, Bruce, and Charlie were running for sheriff. In the election, a total of 15,424 votes were cast. Art received 1006 more than Bruce and 1213 more than Charlie. How many votes did each candidate receive?