8th grade teachers and students from M. I.T went on a field trip to an zoo. Tickets were $5.00 each for teachers and$3.50 each for students, and the group paid
$51.50 in total. A few weeks later, the same group visited a natural history
museum where the tickets cost $20.00 each for teachers and $8.50 each for
students, and the group paid $156.50 in total.
Find the number of teachers and students on the field trips.
A 4 Teachers and 9 Students
4 Teachers and 10 Students
3 Teachers and 9 Students
D None of the above

As there are multiple answers going with trial and error seems good in this case.

A

5.00 + 5.00 + 5.00 + 5.00 = 20.00

3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 = 31.5

20.00 + 31.5 = 51.5

B

5.00 + 5.00 + 5.00 + 5.00 = 20.00

3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 = 35.00

20.00 + 35.00 = 55.00

C

5.00 + 5.00 + 5.00 = 15.00

3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 + 3.50 = 31.5

15.00 + 31.5 =46.5

Knowing that for the first one all A,B, and C were wrong we can determine that D is the answer. But wait if I made one mistake and didn't understand if $156.5 is equivalent to $156.50 that would mean A is correct.

Always recheck your answers and good luck,

Jon

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )