How do you represent each answer as an algebraic expression using the variable mentioned?
A utility company measures gas consumption by the hundred cubic feet, CCF. The company has a three-step rate schedule for gas customers. First, there is a minimum charge of $5.00 per month for up to 3 CCF of gas used. Then, for the next 6 CCF, the charge is $0.75 per CCF. Finally, after 9 CCF, the charge is $0.55 per CCF. Represent the cost of "g" CCF of gas if "g" is greater than 9. Please help...
Let's summarize the question:
0 < g ≤ 3 : cost = 5
when g=3 : cost = 5
3 < g ≤ 9 : cost = 5 + 0.75*(g-3)
when g=9 : cost = 5 + 0.75*6 = 9.60
9 < g : cost = 9.60 + 0.55*(g-9)
Simplify the last expression:
For g≥9 CCF:
cost = 9.60 + 0.55(g-9)
=4.55 + 0.55g
To represent the cost of "g" CCF of gas, we need to break it down into the three steps mentioned in the rate schedule.
Step 1: For up to 3 CCF of gas used, the charge is a minimum of $5.00. This is a fixed cost and does not depend on the amount of gas used. So we can represent it as follows:
Cost for the first 3 CCF (C1) = $5.00
Step 2: For the next 6 CCF, the charge is $0.75 per CCF. This means that for each CCF used in this range, the cost increases by $0.75. We can represent this as follows:
Cost for the next 6 CCF (C2) = $0.75 * (g - 3)
Here, (g - 3) represents the number of CCF of gas used in this range (if g is greater than 3).
Step 3: For any gas usage beyond 9 CCF, the charge is $0.55 per CCF. This means that for each CCF used in this range, the cost increases by $0.55. We can represent this as follows:
Cost for additional gas beyond 9 CCF (C3) = $0.55 * (g - 9)
Here, (g - 9) represents the number of CCF of gas used beyond the initial 9 CCF (if g is greater than 9).
Overall, the algebraic expression for the cost of "g" CCF of gas (if g is greater than 9) can be represented as:
Cost of g CCF of gas = C1 + C2 + C3
= $5.00 + $0.75 * (g - 3) + $0.55 * (g - 9)
This expression captures the three-step rate schedule for gas customers.