Solve Problems 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, and 48.
Because you are practicing a procedure, you must show all of your work. Start with a verbal description and
end with a sentence answering the question.
25.If you add four to three times a number, the result is five squared. What is the number?
; the number is .
26.If you add seven to twice a number, the result is seventeen. What is the number?
27.If you subtract twelve from twice a number, the result is six. What is the number?
Answer
28.If you multiply a number by five and then subtract negative ten, the difference is negative thirty. What is the
number?
29.If six is subtracted from three times a number, the difference is twice the number. What is the number?
Answer
the number is .
30.Find two consecutive integers whose sum is .
31.Find two consecutive even integers whose sum is .
Answer
; the integers are and .
32.The sum of three consecutive integers is . What are the integers?
33.The sum of four consecutive integers is . What are the integers?
Answer
; the integers are and .
34.A house and a lot are appraised at . If the value of the house is five times the value of the lot, how much is
the house worth?
35.A cabinet shop produces two types of custom-made cabinets. If the price of one type of cabinet is four times
the price of the other, and the total price for one of each type of cabinet is , what is the price of each cabinet?
Answer
; the prices of the cabinets are and .
36.To stimulate his daughter in the pursuit of problem solving, a math professor offered to pay her for every
equation correctly solved and to fine her for every incorrect solution. At the end of the first problems of this
problem set, neither owed any money to the other. How many problems did the daughter solve correctly?
37.A professional gambler reported that at the end of the first race at the track he had doubled his money. He
bet on the second race and tripled the money he came with. He bet on the third race and quadrupled his
original bankroll. He bet on the fourth race and lost it, but still had left. With how much money did he start?
Answer
; the gambler started with
38.A -ft pole is to be erected and held in the ground by four guy wires attached at the top. The guy wires are
attached to the ground at a distance of ft from the base of the pole. What is the exact length of each guy wire?
How much wire should be purchased if it cannot be purchased in fractions of a foot?
39.A diagonal brace is to be placed in the wall of a room. The height of the wall is ft, and the wall is ft long.
What is the exact length of the brace, and what is the length of the brace to the nearest foot?
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40.The image shows a right angle triangle. The base of the triangle is labeled as 14 inches, the height of the
triangle is labeled as 8 inches.
Answer
. The exact length of the brace is ; this is approximately .
41.In traveling from Jacksonville to Miami, you pass through Orlando and then through Palm Beach. It is miles
farther from Orlando to Palm Beach than it is from Jacksonville to Orlando. The distance between Jacksonville
and Orlando is miles more than the distance from Palm Beach to Miami. If it is miles from Jacksonville to
Miami, how far is it from Jacksonville to Orlando?
42.The drive from New Orleans to Memphis is miles shorter than the drive from Memphis to Cincinnati, but
miles farther than the drive from Cincinnati to Detroit. If the total highway distance of a New Orleans–
Memphis–Cincinnati–Detroit trip is miles, find the length of the Cincinnati–Detroit leg of the trip.
Answer
; it is from Cincinnati to Detroit.
43.Traveling from San Antonio to Dallas, you first pass through Austin and then Waco before reaching Dallas,
a total distance of miles. From Austin to Waco is miles farther than from San Antonio to Austin, and also miles
farther than from Waco to Dallas. How far is it from Waco to Dallas?
43.Two persons are to run a race, but one can run meters per second, whereas the other can run meters per
second. If the slower runner has a -meter head start, how long will it be before the faster runner catches the
slower runner, if they begin at the same time?
Answer
; the faster runner will catch the slower one in seconds.
44..If the rangefinder on the Enterprise shows a fleeing shuttlecraft km away, how long will it take to catch the
shuttle if the shuttle travels at kph and the Enterprise is traveling at kph?
Starship Enterprise
Starship Enterprise
Photos 12/Alamy
45.A speeding car is traveling at mph when a police car starts pursuit at mph. How long will it take the police
car to catch up to the speeding car? Assume that the speeding car has a -mile head start and that the cars
travel at constant rates.
Answer
; it will take the police car minutes to catch the speeder.
47.Two people walk daily for exercise. One is able to maintain mph and the other only mph. The slower walker
has a mile head start when the other begins, yet they finish together. How far did each walk?
48.Two joggers set out at the same time from their homes miles apart. They agree to meet at a point
somewhere in between in an hour and a half. If the rate of one is mph faster than the rate of the other, find the
rate of each.