The number of hours, H, needed to manufacture X computer monitors is given by the function `H=kX+q`, where k and q are constants. If it takes 270 hours to manufacture 100 computer monitors and 410 hours to manufacture 160 computer monitors, how many minutes are required to manufacture each additional computer monitor?

Answer

To solve the problem, we will follow these steps:

### Step 1: Set up the equations based on the given information.
We know that the number of hours \( H \) needed to manufacture \( X \) computer monitors is given by the equation:
\[ H = kX + q \]
From the problem, we have two scenarios:
1. For 100 monitors, it takes 270 hours:
\[ 270 = k(100) + q \]
This can be rewritten as:
\[ 270 = 100k + q \quad \text{(Equation 1)} \]

2. For 160 monitors, it takes 410 hours:
\[ 410 = k(160) + q \]
This can be rewritten as:
\[ 410 = 160k + q \quad \text{(Equation 2)} \]

### Step 2: Subtract Equation 1 from Equation 2.
We will eliminate \( q \) by subtracting Equation 1 from Equation 2:
\[ (410 - 270) = (160k + q) - (100k + q) \]
This simplifies to:
\[ 140 = 60k \]

### Step 3: Solve for \( k \).
Now, we can solve for \( k \):
\[ k = \frac{140}{60} = \frac{7}{3} \]

### Step 4: Find the time in minutes for each additional monitor.
Since \( k \) represents the hours needed for each additional monitor, we need to convert this to minutes:
\[ \text{Time in minutes} = k \times 60 = \frac{7}{3} \times 60 \]
Calculating this gives:
\[ \frac{7 \times 60}{3} = \frac{420}{3} = 140 \text{ minutes} \]

### Final Answer:
It takes **140 minutes** to manufacture each additional computer monitor.

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