Find the area...

Question

Three islands in the Hawaiian island chain are hawaii(the big island), Maui and Kauai, together, their areas total 5300mi squared. The island of Hawaii is 3293 mi squared larger than the island of Maui and Maui is 177mi squared larger than Kauai. What is the are of each island?

Answer 1

Let

H = area of Hawaii

M = area of Maui

K = area of Kauai

 

From the first sentence, we know

H + M + K = 5300

 

From the 2nd sentence, we know

H = M + 3293

M = K + 177 or K = M - 177

 

We can use these expressions for H and K and substitute them into the equation of the total area of the 3 islands.

H + M + K = 5300

M+3293 + M + M-177 = 5300

 

Combining terms

3M + 3116 = 5300

 

And solving for M

3M = 2184

M = 728

H = M + 3293 = 728 + 3293 = 4021

K = M - 177 = 728 - 177 = 551

 

Checking the solution.

4021 + 728 + 551 = 5300