Solve the following word problem using a linear equation:
John has been recently looking at his phone bill. It costs $2.65 for a 4 minute call and $4.75 for a 10 minute call. How much will it cost John for a 30 minute call?
It looks like he pays 2.10/6 = $0.35 per additional minute, plus a single connection charge (which usually covers the first one or three minutes).
You don't need to know the connection charge to solve this.
30 minutes is an additional 20 beyond a 10 minute call, and would cost 20x0.35 = $7.00 more, or %11.75.
To solve this word problem using a linear equation, we can set up a equation representing the relationship between the cost of the call and the duration of the call.
Let's assume the cost of a 30-minute call is represented by the variable 'x'. We can determine the rate of cost per minute by finding the difference in cost for a 10-minute call and a 4-minute call.
First, we need to find the rate of cost per minute:
Rate of cost per minute = (Cost of a 10-minute call - Cost of a 4-minute call) / (10 minutes - 4 minutes)
Rate of cost per minute = ($4.75 - $2.65) / (10 minutes - 4 minutes)
Simplifying the above expression:
Rate of cost per minute = $2.10 / 6 minutes
Rate of cost per minute = $0.35
Now, we can use this rate to find the cost of a 30-minute call:
Cost of a 30-minute call = Rate of cost per minute * Duration of the call
Cost of a 30-minute call = $0.35 * 30 minutes
Evaluating the expression:
Cost of a 30-minute call = $10.50
Therefore, it will cost John $10.50 for a 30-minute call.