Category 1
The product of two consecutive positive odd integers is 2499. Find the bigger integer.
The bigger integer is 51.
Five times of a positive integer is less than twice its square by 3. Find the integer.
The integer is 3.
The product of two consecutive integers is 3906. Find the integers.
The integers are (62, 63) (-62, -63).
The sum and product of two numbers is 4. What are the numbers?
The numbers are (2, 2).
The product of two consecutive numbers is 12. What are the numbers?
The numbers are (3, 4) (-3, -4).
6x7+ 3x4− 9x3
Factor the greatest common factor from each polynomial.
3x3(2x4 + x − 3)
The area of a rectangular fence is 500 square feet. If the width of the fence is 20 feet, then find its length.
The length is 25 feet.
y2 + 16y + 60
Factor the expression.
(y + 6)(y + 10)
The width of a square is 25 and the area is 125. What is the length?
The length of the square is 5.
z2 − 10z + 21
Factor the expression.
(z - 3)(z - 7)
x2 + 14x + 49
Factor the expression.
(x + 7)(x + 7)
780 students stand in rows and columns. Each row has equal number of students and each column has equal number of students. If the number of students in each row is 4 more than the number of rows, find the number of students in each row.
30 students in each row.
The height of a triangle is 2 mm less than the base. If the area is 60 mm2, find the height and base of the triangle.
The base is 12 mm and the height is 10 mm.
The width of a rectangle is 7 centimeters less than twice its length. Its area is 30 square centimeters. Find the dimensions of the rectangle.
The width is 4 ft and the length is 12 ft.
The width of a rectangle is 7 centimeters less than twice its length. Its area is 30 square centimeters. Find the dimensions of the rectangle.
The width is 5 cm and the length is 6 cm.
A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.
The dimensions of the pool are 15 ft by 30 ft.
An apple orchard contains 85 trees. The number of trees in each row is three less than four times the number of rows. Find the number of rows and the number of trees per row.
The orchard has 5 rows of 17 trees.
The area of a rectangle is twice the area of a square. If the rectangle is 6 inches long, and the width of the rectangle is the same as the length of a side of the square, find the dimensions of both the rectangle and the square.
The square is 3 inches by 3 inches and the rectangle is 3 inches by 6 inches.
The product of two squares is 16. What are the numbers?
22
The sum of the areas of two squares is 234 square inches. Each side of the larger square is five times the length of a side of the smaller square. Find the length of a side of each square.
3 inches and 15 inches.
Suppose that the length of a certain rectangle is 2 1/2 times its width, and the area of that same rectangle is 160 square centimeters. Find the length and width of the rectangle.
20 centimeters and 8 centimeters.
The width of a certain rectangle is three fourths of its length and that the area of this same rectangle is 108 square meters. Find the length and width of the rectangle.
12 meters and 9 meters.
The sum of the areas of a square and a rectangle is 64 square centimeters. The length of the rectangle is 4 centimeters more than a side of the square, and the width of the rectangle is 2 centimeters more than a side of the square. Find the dimensions of the rectangle and the square.
8 centimeters by 6 centimeters and 4 centimeters by 4 centimeters.
A room contains 54 chairs. The number of rows is 3 less than the number of chairs per row. Find the number of rows.
6 rows of chairs.
The length of one leg of a right triangle is 3 centimeters more than the length of the other leg. The length of the hypotenuse is 15 centimeters. Find the lengths of the two legs.
9 centimeters and 12 centimeters.