Solve : `0.3 (3y -4.5) + 2.9 (5.5 -5y) = 1`

Answer

To solve the equation \(0.3(3y - 4.5) + 2.9(5.5 - 5y) = 1\), we will follow these steps:

### Step 1: Distribute the constants inside the parentheses
We will distribute \(0.3\) and \(2.9\) to the terms inside the parentheses.

\[ 0.3(3y) - 0.3(4.5) + 2.9(5.5) - 2.9(5y) = 1 \]

Calculating each term:

\[ 0.9y - 1.35 + 15.95 - 14.5y = 1 \]

### Step 2: Combine like terms
Now, we will combine the \(y\) terms and the constant terms.

\[ (0.9y - 14.5y) + (-1.35 + 15.95) = 1 \]

Calculating the coefficients of \(y\) and the constants:

\[ -13.6y + 14.6 = 1 \]

### Step 3: Isolate the variable term
Next, we will isolate the term with \(y\) by subtracting \(14.6\) from both sides.

\[ -13.6y = 1 - 14.6 \]

Calculating the right side:

\[ -13.6y = -13.6 \]

### Step 4: Solve for \(y\)
Now, divide both sides by \(-13.6\) to solve for \(y\).

\[ y = \frac{-13.6}{-13.6} \]

This simplifies to:

\[ y = 1 \]

### Final Solution
The solution to the equation is:

\[ y = 1 \]