1 a garden is shaped like a rectangle whose perimeter is 250

1. a garden is shaped like a rectangle whose perimeter is 250 ft. The length is 4 times as long as the width. Find the length and the width.

2. when 56 is subtracted from three times avram\'s age, the result is avram\'s age. How old is avram?

3. A fire burned a square shaped fores 14 mi on a side. the area is?

4. if the product of some number and 2 is increased by 6, the result is 4 times the number. Find the number.

Solution

1.   Let the width of the garden be x ft. Then its length is 4x ft. Its perimeter = 2*length +2*width = 2*4x+2*x = 8x+2x = 10x. Therefore, 10x = 250 so that x = 250/10 = 25 ft. Then 4x = 4*25 = 100 ft. Thus, the garden’s length is 100 ft. and its width is 25 ft.

2.   Let Avram’s age be x years. Then 3x-56 = x or, 3x-x = 56 or, 2x = 56 so that x = 56/2 = 28. Thus, Avram is 28 years old.

3.   The area of a square is = (side)². Therefore, the area of the forest is (14)² = 196 sq. miles.

4.   Let x be the required number. Then 2*x +6 = 4*x or, 2x+6 = 4x or, 4x-2x = 6 or, 2x = 6 so that x = 6/2 = 3. Thus, the required number is 3.