solving systems using substitution

Question

the fifth grade teachers took their classes on a field trip to a museum. the first group had 25 students and two teachers and the cost $97.50.  the secomd group had 32 students and three teachers and cost $127.  what is the cost per student and per teacher? 

Answer 1

Nick,

 

Let $s be the cost per student and $t be the cost per teacher

 

For first group 25*s + 2*t = 97.50

For second group 32*s + 3*t = 127

 

Multiply eq 1 by 3 and eq 2 by 2

 

75s + 6t = 292.5

64s + 6t = 254

 

Now subtract these 2 equations

 

s = 3.5

 

Substitute for s = 3.5 in eq. 1

3.5*25 + 2*t = 97.5

 

t = 10

 

So cost per student is $3.5 and cost per teacher is $5