Respuesta :
Answer:
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= [tex]cost\ of \ each\ ticket \times numbers\ of\ tickets[/tex]
∴Art museum trip, [tex]5.5x+3y= 29[/tex] ---- 1st equation
Science museum trip, [tex]22x+11.5y= 113[/tex] ---- 2nd equation
Next using elimination method to find number teacher and students
[tex]5.5x+3y= 29\\22x+11.5y= 113[/tex]
Multiplying both side of 1st equation by 4
∴ [tex]22x+12y= 116\\22x+11.5y= 113[/tex]
changing sign of 2nd equation on both side and solving it.
∴ [tex]0.5y= 3[/tex]
Dividing both side by 0.5
[tex]y= \frac{3}{0.5}= 6[/tex]
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.
[tex]5.5x+3y= 29[/tex]
⇒ [tex]5.5x+3\times 6= 29[/tex]
⇒ [tex]5.5x+18= 29[/tex]
Subtracting both side by 18
⇒ [tex]5.5x= 11[/tex]
Dividing both side by 5.5
⇒ [tex]x= \frac{11}{5.5}= 2[/tex]
Hence, there were 2 teachers on field trips.
