SOLUTION: A gardener needs 6 bushels of a potting medium of 40% peat moss and 60% vermiculite. He decides to add 100% vermiculite to his current potting medium that is 50% peat moss and 50%

Algebra ->  Graphs -> SOLUTION: A gardener needs 6 bushels of a potting medium of 40% peat moss and 60% vermiculite. He decides to add 100% vermiculite to his current potting medium that is 50% peat moss and 50%       Log On


   

Question 939285: A gardener needs 6 bushels of a potting medium of 40% peat moss and 60% vermiculite. He decides to add 100% vermiculite to his current potting medium that is 50% peat moss and 50% vermiculite. The gardener has 5 bushels of the 50% peat moss and 50% vermiculite moss mix. Does he have enough of the 50% peat moss and 50% vermiculite mix to make 6 bushels of the 40% peat moss and 60% vermiculite mix? Explain.
P.S. I am not good at English so it would help me a lot if you can answer this. Thank you.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A gardener needs 6 bushels of a potting medium of 40% peat moss and 60% vermiculite.
He decides to add 100% vermiculite to his current potting medium that is 50% peat moss and 50% vermiculite.
The gardener has 5 bushels of the 50% peat moss and 50% vermiculite moss mix.
Does he have enough of the 50% peat moss and 50% vermiculite mix to make 6 bushels of the 40% peat moss and 60% vermiculite mix? Explain.
:
let x = amt of 100% vermiculite required
then
(6-x) = amt of 50% vermiculite required
:
Write a mixture equation based on the decimal amt of percent vermiculite
x + .50(6-x) = .60(6)
x + 3 - .5x = 3.6
x - .5x = 3.6 - 3
.5x = .6
multiply both sides by 2
x = 1.2 bushels of the 100% vermiculite required
:
Find how much 50:50 stuff he needs
6 - 1.2 = 4.8 bushels, so he has enough
:
See if that checks out
1.2 + .50(4.8) = .60(6)
1.2 + 2.4 = 3.6
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