Problem Solving

The cost C of manufacturing a product can be estimated by the formula C = 0.03 r s t 2 , where r and s are amounts, in pounds, of two major ingredients and t is production time in hours. if r is increased by 50%, s increased by 20% and t decreased by 30%, by approximately what % will the estimated cost of manufacturing the product change.

If 3/x = 2 and y/4 = 3, then (3 + y)/(x + 4) =

If -3 is 6 more than x, what is the value of x/3?

Anne bought a computer for $2,000andthenpaida5percentsalestax,andHenryboughtacomputerfor$1,800 and then paid a 12 percent sales tax. The total amount that Henry paid, including sales tax, was what percent less than the total amount that Anne paid, including sales tax?

An airline passenger is planning a trip that involves three connecting flights that leave from Airports A, B, and C, respectively. The first flight leaves Airport A every hour, beginning at 8:00 a.m., and arrives at Airport B 2 1 2 hours later. The second flight leaves Airport B every 20 minutes, beginning at 8:00 a.m., and arrives at Airport C 1 1 6 ​​​​​​​ hours later. The third flight leaves Airport C every hour, beginning at 8:45 a.m. What is the least total amount of time the passenger must spend between flights if all flights keep to their schedules?

For any integer n greater than 1, [n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between [6 + 2 and [6 + 6, inclusive?

Of the following, which is least ?

A tourist purchased a total of $1,500worthoftraveler\hat{a}€™schecksin$10 and $50denominations,Duringthetripthetouristcashed7checksandthenlostalloftherest.Ifthenumberof$10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?

A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 45 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?

An author received $0.80inroyaltiesforeachofthefirst100,000copiesofherbooksold,and$0.60 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?

Today, Anna is 10 years older than Michelle. If fifteen years ago, Anna was twice as old as Michelle, how old is Michelle today?

If x = (0.08) 2 , y = 1 (0.08) 2 and z = (1 − 0.08) 2 − 1 , which of the following is true?

Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 20% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?

On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s - t)/(t - r) =

Of the 65 cars on a car lot, 45 have air-conditioning, 30 have power windows, and 12 have both air-conditioning and power windows. How many of the cars on the lot have neither air-conditioning nor power windows?

For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula S = 60 k d 2 , where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

Dick and Jane each saved $3,000in1989.In1990Dicksaved8percentmorethanin1989,andtogetherheandJanesavedatotalof$5,000. Approximately what percent less did Jane save in 1990 than in 1989?

A factory that employs 1,000 assembly-line workers pays each of these workers $6 per hour for the first 35 hours worked during a week and 1.25 times that rate for hours worked in excess of 35. What was the total payroll for the assembly line workers for a week in which 60 percent of them worked 20 hours, 30 percent worked 40 hours, and the rest worked 50 hours?

If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S?

Reggie purchased a car costing $8,700.Asadownpaymentheuseda$2,300 insurance settlement and an amount from his savings equal to 15 percent of the difference between the cost of the car and the insurance settlement. If he borrowed the rest of the money needed to purchase the car, how much did he borrow?