Solve for Total: Finding Shirts When 4/5 Are the Right Size

Marcelo organizes his closet.

7 of the shirts are too small for him, while $\frac{4}{5}$ of the shirts are the right size.

How many shirts does Marcelo have?

To solve this problem, we will follow these steps:

• Step 1: Define a variable for the total number of shirts.
• Step 2: Set up an equation using the given information.
• Step 3: Solve the equation to find the total number of shirts.

Now, let's work through each step:
Step 1: Let $x$ be the total number of shirts Marcelo has.

Step 2: According to the problem, $\frac{4}{5}$ of these shirts are the right size. This implies:

$\frac{4}{5}x = x - 7$

This equation states that the number of shirts that are the right size plus the number of too small shirts equals the total number of shirts.

Step 3: Solve the equation:

$\frac{4}{5}x = x - 7$

First, clear the fraction by multiplying both sides by 5:

$4x = 5(x - 7)$

Distribute on the right:

$4x = 5x - 35$

Subtract $5x$ from both sides to isolate the variable on one side:

$4x - 5x = -35$

$-x = -35$

Multiply both sides by -1 to solve for $x$:

$x = 35$

Therefore, the total number of shirts Marcelo has is $35$.