Your old high school pal, Mike Errington, wants to upgrade an old 1976 vintage room air conditioner that is believed to operate at an EER of 7. He is considering a room air conditioner with an EER of 13. What percentage of electricity consumption would be reduced with the new unit?

Provide your answer as a percentage.

The Energy Efficiency Ratio (EER) is the ratio of the cooling capacity (in British Thermal Units, or BTUs) to the power input (in watts). A higher EER means that the air conditioner is more efficient.

If Mike upgrades from an air conditioner with an EER of 7 to one with an EER of 13, he can calculate the percentage reduction in electricity consumption as follows:

Let's say the old air conditioner has a cooling capacity of C1 BTUs and a power input of P1 watts. The new air conditioner has a cooling capacity of C2 BTUs and a power input of P2 watts. Since the cooling capacity is the same for both air conditioners, we have:

C1 = C2

The power input for each air conditioner is:

P1 = C1 / 7 (since the EER is 7)
P2 = C2 / 13 (since the EER is 13)

Substituting C1 = C2, we get:

P1 = C2 / 7
P2 = C2 / 13

The percentage reduction in electricity consumption is:

(P1 - P2) / P1 x 100%

Substituting the expressions for P1 and P2, we get:

[(C2 / 7) - (C2 / 13)] / (C2 / 7) x 100%

Simplifying, we get:

(6 / 91) x 100% ≈ 6.59%

Therefore, if Mike upgrades to an air conditioner with an EER of 13, he can expect to reduce his electricity consumption by about 6.59%.