Solve the following:
`(3t+5)/4-1=(4t-3)/5`

Options

A. `t=17`
B. `t=16`
C. `t=15`
D. `t=14`

Answer

To solve the equation \((3t + 5)/4 - 1 = (4t - 3)/5\), we will follow these steps:

### Step 1: Move the constant to the right side
We start by moving \(-1\) from the left side to the right side of the equation. This changes the equation to:
\[ \frac{3t + 5}{4} = \frac{4t - 3}{5} + 1 \]

### Step 2: Convert 1 to a fraction
To add \(1\) to \(\frac{4t - 3}{5}\), we can write \(1\) as \(\frac{5}{5}\):
\[ \frac{3t + 5}{4} = \frac{4t - 3 + 5}{5} \]
This simplifies to:
\[ \frac{3t + 5}{4} = \frac{4t + 2}{5} \]

### Step 3: Cross-multiply
Now, we cross-multiply to eliminate the fractions:
\[ 5(3t + 5) = 4(4t + 2) \]

### Step 4: Distribute
Distributing both sides gives us:
\[ 15t + 25 = 16t + 8 \]

### Step 5: Rearrange the equation
Next, we will move all terms involving \(t\) to one side and constant terms to the other side:
\[ 15t - 16t = 8 - 25 \]
This simplifies to:
\[ -t = -17 \]

### Step 6: Solve for \(t\)
Finally, we multiply both sides by \(-1\) to solve for \(t\):
\[ t = 17 \]

### Final Answer
The solution to the equation is:
\[ t = 17 \]