Answer:
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
