Math word problem help

Question

Hi!

I have come across this question in my math practice

The nations energy comes from 40% oil, 45% from coal, and the rest from its 450 wind turbines. The government estimates that in a decade, energy demand will have risen by 20%, but oil reserves will have fallen by 10% and coal by 8%.

How many more wind turbines must be built?

As far as my calculations go, in a decade 678 wind turbines will be needed, so the answer would be that 228 more have to be built.

Could you please verify this?

Thank you so much in advance!

Answer 1

Hi there,

unfortunately, the answer is not correct, you will need a total of 1,278 wind turbines in the future, so you need to build additionally 828 wind turbines. You seem to have made the right calculations in terms of the decreases in oil and coal reserves, but not with the new share of those energy sources in a decade. You will need to take into account both effects: The decrease from oil and coal, and the increase of overall energy demand.

When in the past 40% came from oil and the reserves decreased by 10%, it is then 36% of the old energy demand. When the demand increases to 120% but the absolute reserves stay the same, you need to calculate 36% / 120% = 30%. The same way, energy from coal will decrease to 34.5%, resulting in 35.5% share of wind energy in a decade. To come up with the total amount of wind turbines in a decade you need to calculate: 35.5% / 15.0% * 450 turbines * 120%, resulting in 1,278 turbines.

In case you want a more detailed discussion on the math problem, please feel free to contact me directly.

I hope this helps,

Hagen

Answer 2

Hi there,

Looks like Hagen beat me to it :)

My strong recommendation for when you get math is to take a step back and write down the overarching formula/dynamics.

Here, that would be current windpower % divided by current demand compared to future windpower % divided by future demand.