By what percent is Mandy’s bag heavier than Donna’s bag?​

Question

​Three friends each pack a bag for a trip.  Mandy’s bag is <!--[if gte msEquation 12]>20%<![endif]--><!--[if gte vml 1]> <![endif]-->20%20%  heavier than Kathleen’s bag.  Donna’s bag is <!--[if gte msEquation 12]>25%<![endif]--><!--[if gte vml 1]> <![endif]-->25%25%  lighter than Kathleen’s bag.  By what percent is Mandy’s bag heavier than Donna’s bag?​

Answer 1

Mandy's bag is 20% heavier than Kathleen's bag. Donna's bag is 25% lighter than Kathleen's bag. Mandy's bag is what percentage heavier than Donna's bag?

Let M, K and D be the weights of the three bags.

M=1.2K, D=0.75K, M/D=1.2/0.75=1.6, so M=1.6D, so Mandy's bag is 60% heavier than Donna's bag.

Another way of solving this is to give an arbitrary weight to Kathleen's bag, say 100lb. 20% of this is 20lb so Mandy's bag weighs 100+20=120lb. 25% of Kathleen's bag is 25lb so Donna's bag weighs 100-25=75lbs. 120-75=45lb is the difference between the weights of the two bags. Mandy's bag is 45lb heavier than Donna's. Percentage heavier is 45/75×100=⅗×100=60%.