Question

A group of Republicans and Democrats was surveyed and each member was asked whether they liked apple pies or eclairs. 80% of the Republicans liked apple pie, 55% of the Democrats liked eclairs, and 20% of the Republicans who liked apple pie also liked eclairs. If the number of Republicans who liked both desserts is equal to the number of Democrats who liked eclairs, what is one possible value for the number of members of the group

Answer 1

Any multiple of 71 (i.e. 71, 142, 710, etc)

Explanation:

Republicans = R

Democrats = D

Republicans that liked apple pie = 0.80R

Democrats liked eclairs = 0.55D

Republicans who liked apple pie that also liked eclairs = (0.80*0.20)R

If the number of Republicans who liked both desserts is equal to the number of Democrats who liked eclairs, then the following must be true:

`(0.8*0.2)R=0.55D\\0.16R=0.55D\\16R=55D`

Since the number of Republicans and Democrats must be integers, the least number of members possible is 71 (55+16).

Any value that is a multiple of 71 is a possible value for the number of members of the group