Two families went to the event. The first family bought two children's tickets and one adult ticket and paid a total of 8.2 euros. The other family bought three children's tickets and two adult tickets and paid a total of 14.1 euros. Can you tell me how much one child costs and how much one adult ticket costs?

Step-by-step explanation:

step a system of two equations         c = child ticket     a = adult ticket

eq 1)  2c + 1a = 8.2            multiply by 2

eq 2) 3c + 2a = 14.1

I will multiply eq 1 times TWO and subtract eq 2 from eq 1a)

         eq 1a)  4c + 2a = 16.4

          eq 2)  3c + 2a = 14.1

subtract  (4c - 3c) + (2a -2a)  = 16.4 - 14.1  

                    c      +       0       =   2.3 euros     for one child ticket

Now find the adult ticket price,  plug 2.3 for c into eq 1)

     eq 1)  2c + 1a = 8.2

     eq 1)  2(2.3) + 1a = 8.2         solve for a

                 4.6  + a   =  8.2         substract 4.6 from both sides

                             a =  8.2 - 4.6

                               =   3.6 euros    for one adult ticket

double check using eq 2)    we know c and a values

    eq 2)  3c + 2a = 14.1

    eq 2)  3(2.3) + 2(3.6) = 14.1

                   6.9 + 7.2    =  14.1

                          14.1    =  14.1

9 sandwiches per hour

step-by-step explanation:

when we have a rate, we want a 1 in the denominator

27/3 = 9

27 sandwiches/ 3 hours = 9 sandwiches/hour

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,