Let's solve this step by step.
1. Given:
- Initial amount of electrical wire: 40 meters.
- Wire requirements for different fixtures:
- Lamp: 0.45 meters per lamp.
- Wall Light: 0.7 meters per wall light.
- Floor Lamp: 2.6 meters per floor lamp.
2. Fixtures to be wired:
- Number of lamps: 16
- Number of wall lights: 12
- Number of floor lamps: 1
3. Calculate the total wire used for each type of fixture:
- For the lamps:
[tex]\[
\text{Total wire used for lamps} = \text{Number of lamps} \times \text{Wire per lamp}
\][/tex]
[tex]\[
= 16 \times 0.45 = 7.2 \text{ meters}
\][/tex]
- For the wall lights:
[tex]\[
\text{Total wire used for wall lights} = \text{Number of wall lights} \times \text{Wire per wall light}
\][/tex]
[tex]\[
= 12 \times 0.7 = 8.4 \text{ meters}
\][/tex]
- For the floor lamp:
[tex]\[
\text{Total wire used for floor lamp} = \text{Number of floor lamps} \times \text{Wire per floor lamp}
\][/tex]
[tex]\[
= 1 \times 2.6 = 2.6 \text{ meters}
\][/tex]
4. Calculate the total wire used:
[tex]\[
\text{Total wire used} = \text{Wire used for lamps} + \text{Wire used for wall lights} + \text{Wire used for floor lamp}
\][/tex]
[tex]\[
= 7.2 + 8.4 + 2.6 = 18.2 \text{ meters}
\][/tex]
5. Calculate the remaining wire:
[tex]\[
\text{Total wire remaining} = \text{Initial amount of wire} - \text{Total wire used}
\][/tex]
[tex]\[
= 40 - 18.2 = 21.8 \text{ meters}
\][/tex]
Therefore, the amount of electrical wire Mr. Michaels will have after wiring 16 lamps, 12 wall lights, and a floor lamp is:
[tex]\[
\boxed{21.8 \text{ meters}}
\][/tex]
So, the correct answer is 21.8 meters.
