System of Equations

Question

1000 passengers ride the train during the morning hours in Hubbub City. A child's fare is $.50 and an adult fare is $1.50. $1300.00 in fares was collected this morning. How many adults and children rode the train this morning?

 

 

Answer 1

Let A = number of adults who rode the train

 

     C = number of children who rode the train

 

1) A + C = 1000   or rearrange so A = 1000 - C

 

2) $0.50*C + $1.50*A = $1300.00

 

Two equations and two unknowns

 

Substitute eqn 1) into eqn 2) and solve for C:

 

$0.50*C + $1.50*(1000 - C) = $1300     (combine like terms and solve for C)

 

$0.50*C + $1500 -$1.50*C = $1300

 

-$1.00*C = -$200   or $1.00*C = $200

 

C = $200/$1.00 = 200 children

 

A = 1000 - 200 = 800 adults