Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

After 4,000 gallons of water were added to a large water tank that was already filled to ~$\frac{3}{4}$~of its capacity, the tank was then at ~$\frac{4}{5}$~ of its capacity. How many gallons of water does the tank hold when filled to capacity?

If a and b are positive integers and ~$(2^a)^b= 2^3$~, what is the value of ~$2^a2^b$~?

If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar?

Members of a social club met to address 280 newsletters.If they addressed ~$\frac{1}{4}$~of the newsletters during the first hour and~$\frac{2}{5}$~ of the remaining newsletters during the second hour, how many newsletters did they address during the second hour?

Which of the following must be equal to zero for all real numbers x ?

I.-~$\frac{1}{x}$~

II. x + (-x)

III.~$x^0$~

Craig sells major appliances. For each appliance he sells, Craig receives a commission of $50 plus 10 percent of the selling price. During one particular week Craig sold 6 appliances for selling prices totaling $3,620. What was the total of Craig's commissions for that week?

A certain fishing boat is chartered by 6 people who are to contribute equally to the total charter cost of $480. If each person contributes equally to a $150 down payment, how much of the charter cost will each person still owe?