Solve for x: Finding Apples per Tree in (90/x)(x+2)(20) = 3000

Marcos has $x+2$ orchards. In each orchard, there are 20 trees and on each tree there are $\frac{90}{x}$ apples.

If Marcos has 3000 apples in total, then how many apples are there on each tree?

To solve this problem, follow these steps:

• Step 1: Set up the equation using given information.
• Step 2: Simplify and solve the quadratic equation for $x$.
• Step 3: Calculate the apples per tree using the value of $x$.

Now, let's solve the problem:

Step 1: Formulate the equation for the total number of apples:

The total number of apples is given by:

$(x + 2) \times 20 \times \frac{90}{x} = 3000$

Step 2: Simplify the equation:

Expand and rearrange:

$20(x + 2)\frac{90}{x} = 3000$

Calculate the expression:

$\Rightarrow 20 \times (x + 2) \times \frac{90}{x} = 3000$

Simplify to:

$1800 + \frac{3600}{x} = 3000$

Revise by multiplying through by $x$ to eliminate the fraction and solve for $x$:

$1800x + 3600 = 3000x$

Rearranging gives:

$3000x - 1800x = 3600$

$1200x = 3600$

Solving for $x$:

$x = \frac{3600}{1200} = 3$

Step 3: Calculate the apples per tree using $x = 3$:

$\text{Apples per tree} = \frac{90}{x} = \frac{90}{3} = 30$

Therefore, each tree has $\boxed{30}$ apples.