First of all, we're learning how to solve equations with variables on both sides.
Write and solve an equation for the situation.
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?
7 + 5x = 4 + 6x
7-4 = 6x-5x
3 = x
To solve this problem, we can start by defining variables for the unknown quantities. Let's say the length of each section for plants is represented by 'x' feet.
Now, let's calculate the length of each wall:
1. On one wall, we have a 7-ft storage area and 5 sections for plants. The total length of this wall can be represented as 7 + 5x.
2. On the opposite wall, we have a 4-ft storage area and 6 sections for plants. The total length of this wall can be represented as 4 + 6x.
Since the greenhouse is rectangular, the length of one wall should be equal to the length of the other wall. Therefore, we have the following equation:
7 + 5x = 4 + 6x
To solve this equation, we can start by isolating the variable terms on one side. Let's subtract 5x from both sides:
7 = 4 + x
Next, let's subtract 4 from both sides to isolate the variable:
3 = x
Therefore, the length of each section for plants, represented by 'x,' is 3 feet.
To find the length of each wall, we substitute the value of 'x' back into our equations:
- On one wall: 7 + 5(3) = 7 + 15 = 22 feet
- On the opposite wall: 4 + 6(3) = 4 + 18 = 22 feet
Hence, each wall of the greenhouse has a length of 22 feet.