Solve the following equations.
`(y-1)/3-(y-2)/4=1`

Options

A. `y=20`
B. `y=30`
C. `y=10`
D. `y=50`

Answer

To solve the equation \((y-1)/3 - (y-2)/4 = 1\), we will follow these steps:

### Step 1: Find a common denominator
The denominators in the equation are 3 and 4. The least common multiple (LCM) of 3 and 4 is 12.

### Step 2: Rewrite the equation with the common denominator
We will multiply each term by 12 to eliminate the fractions:

\[ 12 \cdot \left(\frac{y-1}{3}\right) - 12 \cdot \left(\frac{y-2}{4}\right) = 12 \cdot 1 \]

This simplifies to:

\[ 4(y-1) - 3(y-2) = 12 \]

### Step 3: Distribute the terms
Now we will distribute the 4 and -3 across the parentheses:

\[ 4y - 4 - 3y + 6 = 12 \]

### Step 4: Combine like terms
Combine the \(y\) terms and the constant terms:

\[ (4y - 3y) + (-4 + 6) = 12 \]

This simplifies to:

\[ y + 2 = 12 \]

### Step 5: Isolate \(y\)
Now, we will isolate \(y\) by subtracting 2 from both sides:

\[ y = 12 - 2 \]

This gives us:

\[ y = 10 \]

### Step 6: Check the solution
To verify, we substitute \(y = 10\) back into the original equation:

\[ \frac{10-1}{3} - \frac{10-2}{4} = 1 \]

Calculating each term:

\[ \frac{9}{3} - \frac{8}{4} = 3 - 2 = 1 \]

Since both sides are equal, our solution is confirmed.

### Final Solution
Thus, the solution to the equation is:

\[ \boxed{10} \]