All of the 3rd grade teachers and students from Gardner Bullis went on a field trip to an art museum. Tickets were $7.50 each for teachers?

Question

All of the 3rd grade teachers and students from Gardner Bullis went on a field trip to an art museum. Tickets were $7.50 each for teachers and $2.50 each for students, and the group paid $37.50 in total.

The next month, the same group visited a natural history museum where the tickets cost $15.00 each for teachers and $10.00 each for students, and the group paid $120.00 in total.

Find the number of teachers and students on the field trips.

Answer 1

Let x be the no of teachers and y be the no of students.



7.50x + 2.50y = 37.50



15x + 10y = 120



MULTIPLY EQUATION 1 BY 4



30x + 10y = 150

15x +10y = 120



SUBTRACT



15x = 30



x = 2

y = 9



ANSWER 2 teachers + 9 students

Answer 2

Whenever questions are phrased in this way i.e. they give you two separate events, i tend to immediately think of simultaneous equations.



Let the number of teachers= x and the number of students= y



For the first museum, it will be 7.5x+2.5y=37.5



For the second museum, it will be 15x+10y=120



To put these two equations together, simply double the first to give: 15x+5y=75



Then do the second equation minus the doubled first equation to give: 5y=45



So y=9, and putting this back into the first equation, x=2



This means there are 2 teachers, and 9 students.

Answer 3

Let X be the number of teachers and Y be the number of students.



For the first trip: 7.5X + 2.5Y = 37.5

For the second trip: 15X + 10Y = 120



Now solve for either variable using the system of equations, I'll multiply the first equation by (-2) to solve for Y first.



-15X - 5Y = -75

15X +10Y = 120 Now add them.

5Y = 45

Y = 9 So now you know there are 9 students, plug that in to either equation to solve for X.



15X + 10(9) = 120

15X = 30

X = 2

So 2 Teachers and 9 students.

Answer 4

X = teachers # , Y= students #

7.5X+2.5Y= 37.5

15X + 10Y= 120

=> first equation times -2=> -15X-5Y=-75

Add the new equation with the second equation=> 5Y=45 <=> Y=9

By replacing Y in any of the first two equation, X=2