Question

Recycling one glass bottle can save enough energy to power an oven for 7.5 minutes. A glass bottle weighs 500 grams. Glass used for recycling costs 5p per kg. How much would it cost to power an oven for 6 hours?

Answer 1

This is a units conversion problem: you have time and you want to convert that to money. Any units conversion problem involves multiplication by 1 in various forms. When you are given 7.5 min = 1 bottle = 500g, you know that (500 g)/(7.5 min) = 1 because the numerator and denominator are equal. (Of course, you are aware that 500 g = 0.500 kg.) The idea is to choose the forms of 1 that cause units you don't want to cancel, leaving only the units you do want.

$6\,h\times \dfrac{0.500\,kg}{7.5\,min}\times \dfrac{60\,min}{1\,h}\times \dfrac{5\,p}{1\,kg}\\\\=\dfrac{6\cdot 0.500\cdot 60\cdot 5\,p}{7.5\cdot 1\cdot 1}=120\,p$

The glass for recycling that would save enough energy to power an oven for 6 hours costs 120p.