During the kite flying competition, Terry's kite flew 6 2/3 times higher than Sue's and 3 1⁄2 times higher than Shannon's. If Shannon's kite reached a height of 84 feet, how high did Terry's kite fly? How high did Sue's kite fly?

Answer 1

To find out how high Terry's kite flew, we first start with Shannon's kite height, which is given as 84 feet.

1. Calculate Terry's kite height compared to Shannon's kite:

   Terry's kite flew 3 1/2 times higher than Shannon's kite.

   \[ \text{Terry's kite height} = 3.5 \times \text{Shannon's kite height} \]

   \[ \text{Terry's kite height} = 3.5 \times 84 \]

   \[ \text{Terry's kite height} = 294 \text{ feet} \]

2. Now calculate Sue's kite height compared to Terry's kite:

   Terry's kite flew 6 2/3 times higher than Sue's kite.

   First, convert 6 2/3 to an improper fraction:

   \[ 6 \frac{2}{3} = \frac{20}{3} \]

   Now, we can express Sue's kite height \( h \) in terms of Terry's kite height:

   \[ \text{Terry's kite height} = \frac{20}{3} \times \text{Sue's kite height} \]

   Setting this equal to Terry's height:

   \[ 294 = \frac{20}{3} \times \text{Sue's kite height} \]

   To isolate Sue's kite height, we multiply both sides by the reciprocal of \( \frac{20}{3} \), which is \( \frac{3}{20} \):

   \[ \text{Sue's kite height} = 294 \times \frac{3}{20} \]

   Calculating this gives:

   \[ \text{Sue's kite height} = \frac{882}{20} = 44.1 \text{ feet} \]

Therefore, the heights of the kites are:

• Terry's kite flew 294 feet high.
• Sue's kite flew 44.1 feet high.