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 100100 pound bag of Vigoro Ultra Turf fertilizer contains 2929 pounds of nitrogen, 33 pounds of phosphoric acid, and 44 pounds of potash. Another type of fertilizer, Parkerâs Premium Starter, has 1818 pounds of nitrogen, 2525 pounds of phosphoric acid, and 66 pounds of potash per 100100 pounds. Determine the amount of each type required to yield a mixture containing the 170170 pounds of nitrogen, 8787 pounds of phosphoric acid, and 3434 pounds of potash

For Vigoro are needed

2929*35.8479 ≅ 104,988.49 (N)

33*3.4351≅113.35 (A)

44*31.2181≅1373.59 (P)

For Parkera are needed

1818*35.8479≅65,171.48 (N)

2525*3.4351≅8673.62 (A)

66*31.2181≅2060.39 (P)

Step-by-step explanation:

we have that in every 100100 pounds of compound nitrogen (N), phosphoric acid (A) and potash (P) are present and that according to the product brand the concentrations vary, therefore:

For Vigoro

2929 N, 33 A, 44 P

For Parkeras

1818 N, 2525 A, 66 P

Now, we need 170170 N, 8787 A and 3434 P of final product containing the components of the types of fertilizers

You can see that the compounds are the same what changes are the proportions from there that

2929N+1818N=170170 ⇒ 4747N=170170 ⇒ N=170170/4747 ≅ 35.8479

33A+2525A=8787 ⇒ 2558A=8787 ⇒ A=8787/2558  ≅ 3.4351

44P+66P = 3434 ⇒ 110P=3434 ⇒ P=3434/110 ≅ 31.2181

Finally

For Vigoro are needed

2929*35.8479 ≅ 104,988.49 (N)

33*3.4351≅113.35 (A)

44*31.2181≅1373.59 (P)

For Parkera are needed

1818*35.8479≅65,171.48 (N)

2525*3.4351≅8673.62 (A)

66*31.2181≅2060.39 (P)

Note: to verify the data, just replace the values in the equations

the first one, all those points on the line just make a strait line.