Fertilizer is sold in 100 pound bags labelled with the amount of nitrogen ( N), phosphoric acid ( P2O5), and potash ( K2O) present. The mixture of these nutrients varies from one type of fertilizer to the next.

For example, a $100$ pound bag of Vigoro Ultra Turf fertilizer contains $29$ pounds of nitrogen, $3$ pounds of phosphoric acid, and $4$ pounds of potash.

Another type of fertilizer, Parker’s Premium Starter, has $18$ pounds of nitrogen, $25$ pounds of phosphoric acid, and $6$ pounds of potash per $100$ pounds.

Determine the amount of each type required to yield a mixture containing the $206$ pounds of nitrogen, $137$ pounds of phosphoric acid, and $46$ pounds of potash.

The mixture contains pounds of Vigoro, and pounds of Parker’s.