Question

The Florida Tourism board surveyed people on their favorite vacation cities. Half of the people said Orlando, 1/4 said Miami, 1/8 said Kissimmee, 1/16 responded Fort Lauderdale, 1/32 said Key West and the rest said Tampa. If 22 people said Tampa, how many people responded Orlando?

Answer 1

Answer: 352 people responded to Orlando.

Explanation:

Let the total number of people be x.

Then, The number of people said Tampa =
`x-((1x)/(2)+\fra1}{4}x+(1)/(8)x+(1)/(16)x+(1)/(32)x)`

`=x-(16x+8x+4x+2x+1x)/(32)\\=x-(31x)/(32)\\=(32x-31x)/(32)\\=(x)/(32)`

⇒The number of people said Tampa =
`(x)/(32)`

Since there are 22 people who respond to Tampa.

`\\\Rightarrow(x)/(32)=22\\\Rightarrow\ x={22*32}\\\Rightarrow\ x=704`

Therefore, the number people responded to Orlando=
`(x)/(2)=(704)/(2)=352`