:( I still cant solve word problem?

Question

In a survey of 220 families planning vacations, 42 planned to vacation exclusively by boat, 37 auto only, 31 just by train, and 21 by plan only. 58 had booked the use of both auto and train, 47 had booked both train and plane, and 54 had booked both auto and plane.How many families planned to use cars, trains, and planes? How many families planned to use exactly two modes of transportation?

Help with solving the problem? Confusion ....

Answer 1

Sorry, I disagree with the previous answer.
Here is my attempt.

Number of families using more than 1 mode of transport =
220 - 42 - 37 - 31 - 21 = 89

Now we are down to three mode of transport again.
Let x be the number of family using all three

A & T only = 58 -x
T & P only = 47 - x
A & P only = 54 - x
Total = 159 - 3x
Including the ones with all three
159 - 2x = 89 x= 35

So number of families use three = 35
number of families using only two = 23 + 12 + 19 = 54

Answer 2

First settle on how lots each guy or woman ate relative to a minimum of one yet another. Dexter ate 2/3 greater suitable than Joe. in terms of proportions this means: for each a million slice that joe eats, Dexter eats a million + 2/3 slices. So.. Joe = J Dexter =J+(2/3)J no count how lots pizza they eat, the comprehensive pizza will continuously be Joe + Dexter. entire = (J) + (J+(2/3)J) entire = 2J + (2/3)J entire = J (2 + 2/3) entire = J(8/3) If the comprehensive pizza eaten exchange into 3. 3 = J(8/3) J = 3 / (8/3) J = (3*3)/8 J = 9/8 J=a million a million/8 Joe eats a million a million/8 pizza Dexter eats something, so which you would be able to calculate: Dexter = J + 2/3(J) utilising Joe's quantity above.. or merely subtract what Joe ate from the three pizzas. 3 - (a million a million/8) = a million 7/8 Dexter eats a million and seven/8 pizzas. A pizza is frequently divided into 8 slices. Joe eats a million pizza and a million slice, Dexter eats a million pizza and seven slices. (the persons asserting the respond is a million 5/6, are asserting Dexter ate 2/3 of a single pizza greater suitable than Joe.. not that Dexter ate 2/3 greater pizza than Joe. i think of they're incorrect.)

Answer 3

Sorry I can't help thinking this problem is incorrect - nothing adds up if the first 4 facts are correct that those different families each only used that mode of transportation.

If that's true - then you are already short a lot of families for the remaining 3 facts you listed and makes me think it is impossible and incorrect to have answers for your two questions.

Good luck if I am wrong! have a good day!

Answer 4

79 families for planes, auto, and train. 159 families for both transportations.