Question

PLEASE HELP!!!!

The photography club decided to go on a field trip to the Andy Warhol museum. They had to break into smaller groups once they got there. The first group had 25 students and 2 teachers. Their cost was $97.50. The second group had 32 students and 3 teachers. Their cost was $127. What is the cost of each student and each teacher?

Part A: Define your variables

Part B: Write a system of equations to represent this situation


Part C: Solve the system of equations you wrote in Part B.


Part D: Interpret what your answer means in context to this situation.


please answer all parts. Thank you for your help :)

Answer 1

A: Let Each Student's share be s
Let Each Teacher's share be t
B: 1st group : 25s + 2t = 97.50 --eqn 1
2nd group : 32s + 3t = 127.0 --eqn 2
C : (25s + 2t = 97.5)*3 = 75s + 6t = 292.5 --eqn3
(32s + 3t = 127.0)*2 = 64s + 6t = 254.0 --eqn4
Subtracting eqn4 from eqn3-->
11s = 38.5
so , s = 3.5
25*3.5 + 2t = 97.5 (from eqn1)
so, t = 5
D: Each student has 3.5$ and Each teacher has 5$ in their share.

Answer 2

Part A: Let x be the cost of each student and y be the cost of each teacher.
Part B: 25x + 2y = 97.5 (1)
32x + 3y = 127 (2)

Part C: Solve simultaneously.
3(1) - 2(2): 75x - 64x = 292.5 - 254
11x = 38.5
x = 38.5/11 = $3.50

Since x = $3.50, 32(3.5) + 3y = 127
112 + 3y = 127
3y = 15
y = $5

Part D: It makes sense, but let's check with the first equation to make sure it satisfies the first equation.

LHS = 25(3.5) + 2(5) = 87.5 + 10 = $97.50, which is true.

Hence, each student costs $3.50 and each teacher costs $5