Answer :
The areas of Hawaii Island, Maui Island and Kauai Island are 4021 square miles, 728 square miles and 551 square miles respectively.
Since it is given that the total area of the three islands in Hawaiian island chain is 5300 square miles and Hawaiian island is 3293 square miles larger than Island of Maui and Kauai Island is 177 square miles less than Maui Island therefore the three equation that we can get are given as:
Total area = H + M + K = 5300 ......(1)
H = M + 3293 ......(2)
K = M - 177 ......(3)
where H, M and K are individual areas of Hawaiian, Maui and Kauai Islands respectively.
Substitute values of equation (2) and (3) in equation (1) we get:
M + 3293 + M + M - 177 = 5300
3M + 3116 = 5300
3M = 2184
=> M = 728 square miles.
Substitute value of M in equation (2) and (3):
H = 728 + 3293 = 4021 square miles.
K = 728 - 177 = 551 square miles.
Thus, the areas are 4021 square miles, 728 square miles and 551 square miles respectively.
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