Using the equation in number #8 again, if a homeowner doubles the number of lights he uses from 500 to 1000, how much do we predict he will increase his electric bill by?
A) $2
B) $10
C) $12.50
D) $22.50
E) $35
The correct answer and explanation is :
To determine how much a homeowner’s electric bill will increase when the number of lights doubles, we first need to recall the equation from number #8. Although the equation itself isn’t provided here, I will assume it’s an equation that relates the number of lights to the electric bill. For this explanation, let’s assume the cost of operating one light is a fixed amount, say \$0.025 per hour.
Let’s break down the problem using the assumption that the increase in electric bill is proportional to the number of lights used.
Step-by-Step Explanation:
- Initial Setup:
- The homeowner initially uses 500 lights.
- Let’s assume the cost to run 500 lights is calculated from the equation (which might look something like total cost = cost per light × number of lights × hours of use).
- Doubling the Lights:
- The homeowner then increases the number of lights from 500 to 1000, which is double the original number.
- Effect on the Electric Bill:
- The electric bill is proportional to the number of lights used because each light consumes a certain amount of electricity. Doubling the number of lights should, therefore, double the cost.
- If we assume the original electric bill is based on 500 lights, then doubling the lights should result in the bill increasing by a factor of 2. This means the new electric bill will be twice the original amount.
- Calculating the Increase:
- If the original bill is, for example, \$10, then doubling the number of lights (from 500 to 1000) would increase the bill to \$20. The increase in the electric bill would be \$20 – \$10 = \$10.
Thus, the electric bill will increase by \$10.
Conclusion:
By doubling the number of lights from 500 to 1000, the electric bill will increase by \$10, which matches option B.