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 mix. Does he have enough of the 50/50 mix to make 6 bushels of the 40% peat moss and 60% vermiculite mix? Explain.
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He will use x bushels of 50%, and 6 - x bushels of 100%. The result will be: .50 * x + 6 - x .6 * 6 3.6 -x/2 -2.4 x 4.8 4.8 bushels of 50/50 mix contains 2.4 bushels of pure vermiculite adding 1.2 to make it 6 and you have (2.4 + 1.2) / 6 3.6 / 6 bushels of pure vermiculite 60%. He can also do it this way, using his whole 5 bushels: Let x amount of 100% vermiculite to add. 5 bushels of 50% vermiculite 2.5 bushels of pure vermiculite. 2.5 + x .60 * (5 + x) [ existing vermiculite + added 60% of total ] 2.5 + x 3 + .60 x .40 x .5 x 1.25 bushels added. Then he will have 6 1/4 bushels of the new mix. which will be 60% vermiculite. ( 3.75 / 6.25 0.60 ) If he then throws away 1/4 bushel of the new mix, he will have the desired mix in the desired quantity.
