how many adults and how many kids

Question

at a fair tickets cost 4 dollars for an adult and 1.50 per kid when the total revenue of that day is $705 how many adults attended and how many kids attended

Answer 1

4a + 1.5k = 705

a + k = t

1.5a + 1.5k = 1.5t

subtract last from 1st equation

2.5a = 705- 1.5t

a = 705/2.5 - 1.5t/2.5 = number of adults = 7050/25 - .6t = 282 - .6t where t= total attending adults + kids

so number of adults is less than 282, at most 281 adults

k = t -a = t-282, total is at least 282, so k is more than zero