Daily Exam 3 – Algebra 2

A Roman statue is three times as old as a Florentine statue. One hundred years from now the Roman statue will be twice as old. How old is the Raman statue?

Two planes leave Kansas City at 1 P.M. Plane A heads east at 450 mph and plane B heads due west at 600 mph. How long will it be before the planes are 2100 miles?

A boat has a speed of 15 mph in still water. It travels downstream from Greentown to Glenavon in two-fifths of an hour. It then goes back upstream from Glenavon to Cambria, which is 2 miles downstream from Greentown, in three-fifths of an hours. Find the rate of the current.

Seymour is twice as old as Cassandra. If 16 is added to Cassandra’s age and 16 is subtracted from Seymour’s age, their ages will then be equal. What are their present ages?

One machine can complete a job in 10 minutes. If the same job is done by this machine and an older machine working together, the job can be completed in 6 minutes. How long would it take the older machine to do the job alone?

Jones can paint a car in 8 hours. Smith can paint the same car in 6 hours. They start to paint the car together. After 2 hours, Jones leaves for lunch and Smith finishes painting the car lone. How long does it take Smith to finish?

Three times the first of three consecutive odd integers is three more than twice the third. Find the third integer.

The ten’s digit of a certain two digit number exceeds the unit’s digit by four and is one less than twice the unit’s digtt. Find the number.

If w varies directly as the product of x and y and inversely as the square of z and that w = 4 when x = 2, y = 6 and z = 3. Find w when x = 1, y = 4 and z = 2.

The vibration frequency of a string varies as the square root of the tension and inversely as the product of the length and diameter of the string. If the string is 3 feet long and 0.03-inch in diameter vibrates at 720 times per second under 90 pounds tension, at what frequency will a 2 feet long, 0.025-inch string vibrate under 2500 pounds tension?

If 3 is subtracted from the numerator of a certain fraction, the value of the fraction becomes 3/5. If one is subtracted from the denominator of the same fraction, the value of the fraction becomes 2/3. Find the original fraction.

The sum of the digits of a 3-digit number is 14. The hundred’s digit being 4 times the unit’s digit. If 594 is subtracted from the number, the order of the digits will be reversed. Find the number.

The cost of labor varies jointly as the number of workers and the number of days they work. If 8 men working 9 days each are paid P576, in how many days it take 6 men to earn P624?

Two thousand kg of steel containing 8% nickel is to be made by mixing steel containing 14% nickel with another steel containing 6% nickel. How much of the steel containing 14% nickel is needed?

Find two consecutive odd numbers such that thrice the smaller number exceeds the larger by 12.

The difference of the cubes of two positive numbers is 2402 and the cube of their difference is 8. Find the bigger number.

A boatman rows to a place 48 km distant and back in 14 hours; he finds that he can row 4 km with the stream in the same time as 3 km against the stream; find the rate of the stream.

Find the number such that their sum multiplied by the sum of their squares is 65, and their difference multiplied by the difference of their squares is 5.

In a commercial survey involving 1,000 persons on brand preference, 120 were found to prefer brand x only, 200 prefer brand y only, 150 prefer brand z only, 370 prefer either brand x or y but not z, 450 prefer brand y or z but not x, and 420 prefer either brand z or x but not y. How many persons have no brand preference, satisfied with any of the 3 brands?

Find the sum of the first 40 even numbers.

Find the sum of all odd integers between 100 and 1000.

Find the sum of the integers between 2 and 100 which is divided by 3.

The first and the last term of a G.P is equal to 6 and 486 respectively. If the sum of all terms is 726, find the number of terms.

A body dropped from a height falls 16 m during the first second, 48 m in the next second; 144 m on the third second and so on. Find how far the body falls during the 7th second.

The sides of a square is 6 cm. long. A second square is inscribed by joining the midpoint of the sides of the second square and so on. Find the sum of the areas of the infinite number of inscribed squares thus formed.