Yolanda decides to grow apples on her farm.
In the first orchard, there are 7 trees per m². In the second orchard, there are 3 trees per m². In the third orchard, there is a single tree for every 4 m². Additionally, there are another 8 trees around the farm. The surface areas of the orchards are the same.
If Yolanda had grown the trees in a single orchard with a surface area of 516.5 m², so that every 1221 m² had one tree, the number of trees would remain the same.
What is the surface area of each orchard?
Let's solve the problem using the information given:
- Calculate the number of trees in each orchard based on their densities:
- Orchard 1 has 7x trees.
- Orchard 2 has 3x trees.
- Orchard 3 has 0.25x trees.
- The total number of trees from the three orchards is:
7x+3x+0.25x=10.25x.
- Including the additional 8 trees around the farm, the formula becomes:
10.25x+8.
- In the hypothetical scenario, the number of trees is:
1221516.5.
- Setting these equal gives:
10.25x+8=1221516.5.
- First, calculate 1221516.5:
1221516.5≈0.423.
- Simplify the equation:
10.25x+8=0.423,
10.25x=0.423−8,
10.25x=−7.577,
x≈100.
Therefore, the surface area of each orchard is 100 m².