An architect is designing a rectangular greenhouse. Along one wall is a 7- ft storage area and 5 sections for different kinds of plants. On the opposite wall is a 4-ft storage area and 6 sections for plants. All of the sections for plants are of equal length. What is the length of each wall?

Question

anonymous · Answer

All the sections for plants are of equal length, so call that length x. On one wall we have a 7 ft storage area and 5 sections of length x, so the total length is 7 + 5x. On the other wall we have a 4 ft storage area and 6 sections of length x, so the total length is 4 + 6x.

The lengths of the walls are equal, so we have 7 + 5x = 4 + 6x. If we subtract 5x from both sides we get 7 + 5x - 5x = 4 + 6x - 5x, or 7 = 4 + x. Then subtract 4 from each side: 7 - 4 = 4 + x - 4 or 3 = x. So each section is 3 feet long.

to check the answer: One wall has a 7 ft storage area plus 5 sections of 3 feet each, so total length is 7  + 3 * 5 = 7 + 15 = 22. The other wall has a 4 ft storage area plus 6 sections of 3 feet each, so total length is 4 + 6 * 3 = 4 + 18 = 22, same as the first.