Percentage of percent change

Question

40% of the weight of wet timber is water.

How many percentages does the water percentage need to decrease for the water percentage to hit 8%?

My calculations get me 80% but my homework answers tell me I should get an answer of 87%.

I understand that after the water percentage drops if affects the total weight aswell, just can't get my head around to form an equation

How do I get to that 87%?

Answer 1

choose a weight for the wood, say, 100 lbs

40% is water so 60% is wood

therefore 60 lbs is wood

if the water percentage is 8%, then 92% of the weight is wood

but there is 60 lbs of wood

92% of the total weight is 60 lbs of wood

92% of what number is 60 ?

0.92*n=60 where n=the total weight of the tree

n=60/0.92

n=65.2174 lbs is the total weight of the tree

60 lbs is wood

so 5.2174 lbs is water

you went from 40 lbs of water to 5.2174 lbs of water

40-5.2174=34.7826 lbs

34.7826/40=0.86956≈0.87=87%

Answer 2

choose a weight for the wood, say, 100 lbs

40% is water so 60% is wood

therefore 60 lbs is wood

if the water percentage is 8%, then 92% of the weight is wood

but there is 60 lbs of wood

92% of the total weight is 60 lbs of wood

92% of what number is 60 ?

0.92*n=60 where n=the total weight of the tree

n=60/0.92

n=65.2174 lbs is the total weight of the tree

60 lbs is wood

so 5.2174 lbs is water

you went from 40 lbs of water to 5.2174 lbs of water

40-5.2174=34.7826 lbs

34.7826/40=0.86956≈0.87=87%