Solve the Mixed Number Equation: 2⅖z - (z÷y/4÷y/3 - 13z)

To solve this problem, we'll follow these steps:

• Step 1: Simplify the term $z : \frac{y}{4} : \frac{y}{3}$.
• Step 2: Use the distributive property to expand and simplify the expression.
• Step 3: Combine like terms.

Let's go through these steps in detail:

Step 1: Simplify the term $z : \frac{y}{4} : \frac{y}{3}$:

This expression can be simplified as $z \times \frac{4}{y} \times \frac{3}{y} = z \times \frac{12}{y^2} = \frac{12z}{y^2}$.

Step 2: Substitute this back into the original expression:

$2\frac{2}{5}z - ( \frac{12z}{y^2} - 13z )$.

Distribute the negative sign over the terms inside the parentheses:

$2\frac{2}{5}z - \frac{12z}{y^2} + 13z$.

Step 3: Combine like terms:

Convert the mixed number $2\frac{2}{5}$ into an improper fraction: $2\frac{2}{5} = \frac{12}{5}$.

Now, combine the like terms $\frac{12}{5}z + 13z$:

$\frac{12}{5}z + 13z = \left( \frac{12}{5} + \frac{65}{5} \right)z = \frac{77}{5}z = 15\frac{2}{5}z$.

Therefore, the simplified expression is:

$15\frac{2}{5}z - \frac{12z}{y^2}$.

Thus, the correct answer to the problem is $\boxed{15\frac{2}{5}z - \frac{12z}{y^2}}$, and this matches the answer choice 1.