Population word problem

Question

In 1984, the populations of 1,210 different towns were all different than their populations in 1980. The number of populations that were greater in 1984 than in 1980 was 20% greater than the number that were greater in 1980 than in 1984. How many of the towns had a greater population in 1984 than in 1980?

Answer 1

pop. In 1984 is less         x

pop. In 1984 is equal     0

pop. In 1984 is greater    y

 TOTAL                          1210

“all different” puts a 0 in the “equal to” row.

“The number of populations that were greater in 1984 than in 1980 was 20% greater than the number that were greater in 1980 than in 1984”   means y = 1.2x

Obviously,  x + 0 + y = 1210

 x + 1.2x = 1210   [substitute value for y]

 2.2x = 1210

  x = 2010/2.2

  x = 550

y = 1.2x

so, y = 660   [greater population in 1984 than in 1980]

Check:

Does x + y = 1210   ?

550 + 660 = 1210   ?

   1210 = 1210  ?yes