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Word Problems
I.
II.
Integer Problems
1.
Find 3 consecutive integers if the sum of the first and third is 128.
2.
Find 4 consecutive odd integers whose sum is 152.
3.
Find 4 consecutive even integers if the sum of the first and third is 4 more
than the second.
4.
Find 3 consecutive even integers such that the sum of the first and last
integers is three times the second integer diminished by 14.
Angle Problems
5. An angle is 12 degrees more than its complement. Find the measure of the
complement.
6.
An angle is 15 degrees less than twice its complement. Find the angles.
7.
Find two supplementary angles if one is four times the other.
8. How large is an angle whose supplement is 21 degrees less than four times its
complement.
9.
One angle of a triangle exceeds another by 23 degrees. The third angle is 6
degrees less than the sum of the other two. Find the angles.
III. Geometry Problems
10.
Each leg of an isosceles triangle exceeds twice the base by 5 inches. Find
each side of the triangle if the perimeter is 5 feet.
11.
If one side of a square is increased by 8 feet and an adjacent side decreased
by 2 feet, a rectangle is formed whose perimeter is 40 feet. Find the length
of a side of the square.
12.
The length of a certain rectangle is twice its width. If the length is decreased
by 3 cm, the area of the resulting rectangle is 12 sq. cm less than the area of
the original rectangle. Find the original dimensions.
13.
IV.
The area of a square is 18 sq in less than twice the area of a triangle. The
base of the triangle is 3 in longer and the altitude is the same length as the
side of the square. Find the side of the square.
Motion Problems
14.
Mr. Rush and Mr. Slow arrange to meet at an airport that is between their
home airports. Mr. Rush’s jet travels at 600 mph; Mr. Slow’s jet travels at
320 mph. They leave their home airports, which are 1380 miles apart, at the
same time. In how many hours will they meet?
15.
An airplane which maintains an average speed of 350 mph passed an airport
at 8 AM. A jet, following that course at a different altitude, passed the same
airport at 10 AM and overtook the airplane at 12 noon. At what rate was the
jet flying?
16.
A man leaves his home and drives to a convention at an average rate of 50
mph. Upon arrival, he found a telegram advising him to return home at
once. He catches a plane that takes him back at an average rate of 300 mph.
3
If the total traveling time was 1 hr., how long did it take him to fly back?
4
How far from his home was the convention?
17.
A train left Ambler at 9:00AM traveling 50 mph. At 1:00 a private plane
left Wings field and traveled in the same direction at 300 mph. At what
time did the plane overtake the train?
18.
At a certain time, two airplanes start from the same airport and travel in
opposite directions at 350 mph and 325 mph respectively. In how many
hours will they be 2025 miles apart?
19.
A troop of scouts hiked to the County Scout Cabin at Camp Delmont at the
rate of 2 mph. They rode back to scout headquarters at Valley Forge by car
at 18 mph. If the round trip took 10 hours, how far is headquarters from the
cabin?