The cost of hiring a van is partly constant and partly varies with the time spent. it cost 180 for a 2 hours hire and 450 for a 7 hours. Find the cost for 10 hours

Answer 1

Let the cost of hiring the van be expressed in the form:

\[ C = a + bt \]

where:

• \( C \) is the total cost,
• \( a \) is the constant cost,
• \( b \) is the variable cost per hour, and
• \( t \) is the number of hours hired.

From the information provided, we have two equations:

1. For 2 hours: \[ 180 = a + 2b \quad \text{(1)} \]

2. For 7 hours: \[ 450 = a + 7b \quad \text{(2)} \]

Now we can solve these equations simultaneously.

First, let's subtract equation (1) from equation (2) to eliminate \( a \):

\[ 450 - 180 = (a + 7b) - (a + 2b) \] \[ 270 = 5b \] \[ b = \frac{270}{5} = 54 \]

Now that we have \( b \), let's substitute \( b \) back into equation (1) to find \( a \):

\[ 180 = a + 2(54) \] \[ 180 = a + 108 \] \[ a = 180 - 108 = 72 \]

Now we have \( a = 72 \) and \( b = 54 \).

Next, we can find the cost for 10 hours by substituting \( a \) and \( b \) into the cost formula:

\[ C = a + bt \] \[ C = 72 + 54 \times 10 \] \[ C = 72 + 540 \] \[ C = 612 \]

Thus, the cost for hiring the van for 10 hours is 612.