`17s+20t=59`
`30s+40t=110`
In the system of equations above, what is the value of t in terms of x?

Options

A. `(2s)/5`
B. `s/5`
C. `5/(2s)`
D. `5/s`

Answer

To solve the system of equations given by:

1. \( 17s + 20t = 59 \) (Equation 1)
2. \( 30s + 40t = 110 \) (Equation 2)

we need to find the value of \( t \) in terms of \( s \).

### Step 1: Multiply the first equation by 2
We can multiply the entire first equation by 2 to make the coefficients of \( t \) in both equations the same.

\[ 2(17s + 20t) = 2(59) \]

This simplifies to:

\[ 34s + 40t = 118 \quad \text{(Equation 3)} \]

### Step 2: Subtract Equation 2 from Equation 3
Now we will subtract Equation 2 from Equation 3:

\[ (34s + 40t) - (30s + 40t) = 118 - 110 \]

This simplifies to:

\[ 34s - 30s + 40t - 40t = 8 \]

\[ 4s = 8 \]

### Step 3: Solve for \( s \)
Now, we can solve for \( s \):

\[ s = \frac{8}{4} = 2 \]

### Step 4: Substitute \( s \) back into Equation 1
Next, we substitute \( s = 2 \) back into Equation 1 to find \( t \):

\[ 17(2) + 20t = 59 \]

This simplifies to:

\[ 34 + 20t = 59 \]

### Step 5: Isolate \( t \)
Now, isolate \( t \):

\[ 20t = 59 - 34 \]

\[ 20t = 25 \]

\[ t = \frac{25}{20} = \frac{5}{4} \]

### Step 6: Express \( t \) in terms of \( s \)
Now, we want to express \( t \) in terms of \( s \). We know \( s = 2 \) and \( t = \frac{5}{4} \).

To express \( t \) in terms of \( s \):

\[ t = \frac{5}{4} \quad \text{and} \quad s = 2 \]

We can write:

\[ t = \frac{5}{2s} \]

### Final Result
Thus, the value of \( t \) in terms of \( s \) is:

\[ t = \frac{5}{2}s \]