Solve `0. 5 gamma + 0. 75 y = 125`

Answer

To solve the equation \(0.5y + 0.75y = 125\), we will follow these steps:

### Step 1: Write the equation
We start with the equation:
\[ 0.5y + 0.75y = 125 \]

### Step 2: Convert decimals to fractions
Convert \(0.5\) and \(0.75\) into fractions:
\[ 0.5 = \frac{1}{2} \quad \text{and} \quad 0.75 = \frac{3}{4} \]
So, we can rewrite the equation as:
\[ \frac{1}{2}y + \frac{3}{4}y = 125 \]

### Step 3: Find a common denominator
The common denominator for \(2\) and \(4\) is \(4\). We will convert \(\frac{1}{2}y\) to have a denominator of \(4\):
\[ \frac{1}{2}y = \frac{2}{4}y \]
Now the equation becomes:
\[ \frac{2}{4}y + \frac{3}{4}y = 125 \]

### Step 4: Combine like terms
Now we can combine the terms on the left side:
\[ \frac{2 + 3}{4}y = 125 \]
This simplifies to:
\[ \frac{5}{4}y = 125 \]

### Step 5: Solve for \(y\)
To isolate \(y\), multiply both sides by the reciprocal of \(\frac{5}{4}\), which is \(\frac{4}{5}\):
\[ y = 125 \times \frac{4}{5} \]

### Step 6: Calculate the value
Now we can calculate:
\[ y = 125 \times \frac{4}{5} = 125 \times 0.8 = 100 \]

### Final Answer
Thus, the value of \(y\) is:
\[ \boxed{100} \]