Questions: Cell phone towers vary in height from 50 to 200 feet high. If two cell phone towers have a total height of 302 feet and one of the towers is 42 feet taller than the other, find the height of both of the towers. The shorter tower has a height of feet. The taller tower has a height of feet.

Solution Steps

Let the height of the shorter tower be \( x \) feet. Then, the height of the taller tower is \( x + 42 \) feet.

The total height of both towers is 302 feet. Therefore: \[ x + (x + 42) = 302 \]

Combine like terms: \[ 2x + 42 = 302 \] Subtract 42 from both sides: \[ 2x = 260 \] Divide both sides by 2: \[ x = 130 \]

The height of the taller tower is: \[ x + 42 = 130 + 42 = 172 \]

Final Answer