All of the 4th grade teachers and students from cambridge went on a field trip to an art museum. tickets were $5.50 per teacher and $3.00 for each student. this group paid $29.00 in total. the next month, the same group visited a science museum where the tickets were $22.00 for teachers and $11.50 for students. the group paid $113.00 in total. find the number of teachers and students on the field trips.

Students= 6

Teachers= 2

Step-by-step explanation:

Given: Art museum trip:

           Cost of ticket= $5.5 per teacher and $3 per student.

           Total amount paid= $29.

           Science trip:

           Cost of ticket= $22 per teacher and $11.5 per student.

           Total amount paid= $113.

Lets assume number of teacher be "x" and number of students be "y".

Now, forming an equation for cost of each trip.

we know, total cost=

∴Art museum trip, ---- 1st equation

Science museum trip, ---- 2nd equation

Next using elimination method to find number teacher and students

Multiplying both side of 1st equation by 4

∴

changing sign of 2nd equation on both side and solving it.

∴

Dividing both side by 0.5

Hence, number of students on field trip was 6.

Subtituting the value of y in 1st equation to find the number of teachers in field trip.

⇒

⇒

Subtracting both side by 18

⇒

Dividing both side by 5.5

⇒

Hence, there were 2 teachers on field trips.