state A, B and C have hosted a certain sporting event a total of 75 times. state A had hosted the sporting event 9 more times then state C. together, state A and state C have hosted five more than four times the number of this sporting event that state b hosted. determine the number of times this sporting even was hosted by each of the three states

Step-by-step explanation:

Total events = 75

A + B + C = 75  (I)

State A had hosted the sporting event 9 more times then state C.

A = C + 9 (II)

Together, state A and state C have hosted five more than four times the number of this sporting event that state b hosted.

A + C = 4B + 5  (III)

Substitute A = C + 9 in (III)

C + 9 + C = 4B + 5

   2C + 4 = 4B  + 5

        2C  = 4B + 5 - 9

       2C  = 4B - 4

Divide the whole equation by 2

   2C/2  = 4B/2  - 4/2

        C = 2B  - 2 (a)

Plugin the C = 2B - 2 in (II)

A = C +  9

A = 2B - 2 + 9

A = 2B + 7 (b)

Plugin the value of A & C from (a) & (b) in equation (I)

A + B + C = 75

2B + 7 + B + 2B - 2 = 75

Add the like terms

2B + B + 2B + 7 - 2 = 75

5B + 5 = 75

5B = 75 - 5

5B = 70

B = 70/5

B = 14

Plug in B value in equation (a)

C = 2B - 2

C = 2*14 -2

  = 28 - 2

C = 26

Plugin B value in equation (b)

A = 2B + 7

  = 2*14 + 7

 = 28 + 7

A = 35

State A has hosted 35 times

State B has hosted  14 times

State C has hosted 26 times