Question

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.

Answer 1

Students= 6

Teachers= 2

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=
`cost\ of \ each\ ticket * numbers\ of\ tickets`

∴Art museum trip,
`5.5x+3y= 29` ---- 1st equation

Science museum trip,
`22x+11.5y= 113` ---- 2nd equation

Next using elimination method to find number teacher and students

`5.5x+3y= 29\\22x+11.5y= 113`

Multiplying both side of 1st equation by 4

∴
`22x+12y= 116\\22x+11.5y= 113`

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

∴
`0.5y= 3`

Dividing both side by 0.5

`y= (3)/(0.5)= 6`

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.

`5.5x+3y= 29`

⇒
`5.5x+3* 6= 29`

⇒
`5.5x+18= 29`

Subtracting both side by 18

⇒
`5.5x= 11`

Dividing both side by 5.5

⇒
`x= (11)/(5.5)= 2`

Hence, there were 2 teachers on field trips.