Question

Fertilizer with weed control costing $38 per pound bag is to be mixed with less expensive fertilizer costing $6 per 50 pound bag to make 16 bags of fertilizer that can be sold for $26 per bag. How many bags of cheaper fertilizer should be used

Answer 1

There seems to be an error. A fertilizer bag will weigh 1 pound or 50 pounds. We presume that the bag of costlier fertilizer bag will also weigh 50 pounds. Let x bags of fertilizer with weed control be mixed with y bags of less expensive fertilizer to make 16 bags of fertilizer that can be sold for $ 26 per bag. Then we have x+y = 16…(1).

Also the price of x bags of costlier fertilizer is 38x and the price of y bags of less expensive fertilizer is 6y. Further, the cost of 16 bags of fertilizer costing $26 per bag is $26*16 = $ 416. Hence 38x+6y = 416 or, on dividing both the sides by 2, we get 19x+3y = 208…(2)

From the 1^st equation, we have y = 16-x. On substituting y = 16-x in the 2^nd equation, we get 19x+3(16-x) = 208 or, 19x+48-3x = 208 or, 16x = 208-48 = 160 so that x = 160/16 = 10. Then y = 16-x = 16-10 = 6.

Thus, 10 bags of fertilizer with weed control should be mixed with 6 bags of less expensive fertilizer to make 16 bags of fertilizer that can be sold for $ 26 per bag.