Algebra question again

Question

A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by $12.

 

a) What is the fixed total cost to charter the aircraft?

b) What is the cost per person if 40 people charter the aircraft?

Answer 1

Let x = the per person cost

 

36(x + 12) = 40x

 

36x + 432 = 40x

 

432 = 4x

 

x = 108

 

The per person cost for 40 people is $108

 

The fixed total cost is 40 * 108 = $4,320

Answer 2

Let X be the price to rent the aircraft.

 

X/36 - 12 = x/40

 

Multiplying everything by The common denominator

of 36 * 40 = 1440 causes the fractions to drop out.

 

40X - 17280 = 36X

 

40X - 36X - 17280 = 0

 

4X = 17280

 

X = 4320

 

Check: 4320/40 = 108

          4320/36 = 120 

Which is a $12 difference

 

It costs $4320 to rent the aircraft.

40 people pay $108 each.

36 people pay $120 each