Income Tax: Problems and Solutions

Solve by finding the root of an equation in just one unknown.

1. A rope 75 feet long is cut into two pieces where one is 11 feet long than the other. Find their lengths.

Let x = shorter piece’s lenght x + 11 = longer piece’s lenght

Solution: x + x +11 = 75 2x = 75 – 11 2x = 64 2x = 64 2 2 x = 32 x + 11 = 32 + 11 = 43

2. Find the dimensions of a rectangle where the altitude is four seventh of of the base and the perimeter is 330 feet.

Let x = length of the base x = length of the altitude

since the perimeter = 300

Solution: 330 = 2x + 2 ( x) 330 = 2x+ x 7 [ 330 = 2x+ x ] 7 2310 = 14x +8x 2310 = 22x 2310 = 22x 22 22 x = 105 32 + 11 = 43 ft. x = (43) = 60 ft.

3. Find two consecutive integers whose sum is 73.

Let x = first integer x + 1 = second integer

Solution: x + x +1 = 73 2x = 75 – 1 2x = 74 2x = 74 2 2 x = 36 x + 1 = 36 + 1 = 37

4. Find two consecutive odd positive integers whose squares differ by 64.

Let x = first odd integer x + 2 = second odd integer

Solution: (x + 2)2 – x2 = 64 x2 + 4x +4 - x2 = 64 x2 + 4x +4 - x2 = 64 4x = 64 - 4 4x = 60 4x = 60 4 4 x = 15 x + 2 = 15 + 2 = 17

5. One dimension of a rectangle is 4/5 of the other. Find the dimension if the perimeter of the rectangle becomes 62 feet when each imension is increased by 2 feet.

Let x = lenght of the rectangle (x+2 when increased) x = width of the rectangle ( x + 2 when increases)

Solution: P = 2l + 2w 62 = 2(x + 2) + 2 (