Question

For example, a 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 bag. Determine the number of bags of each type required to yield a mixture containing 181 pounds of nitrogen, 65 pounds of phosphoric acid, and 32 pounds of potash.

Answer 1

When we are given information on different products and are asked to calculate a result from these, we are generally being provided with equations, in this case to calculate the number of bags required to make the requested mixture we have the following equations:

$29A+18B=181\\3A+25B=65\\4A+6B=32$

Where A and B represent the number of bosas of each fertilizer brand, as we have two unknowns we will use two equations like this:

$1) 3A+25B=65\\2) 4A+6B=32$

One incognita is cleared depending on the other

$2) 4A+6B=32\\4A=32-6B\\A=8-\frac{6}{4} B$

The values ​​obtained in the second are replaced

$1) 3A+25B=65\\3(8-\frac{6}{4} B)+25B=65\\24-\frac{18}{4} B+25B=65\\B(-\frac{18}{4}+\frac{100}{4})=41\\B(\frac{82}{4})=41\\B(\frac{41}{2})=41\\B=2$

With the value of B it is replaced in the first one to obtain the value of A:

$A=8-\frac{6}{4} B\\A=8-\frac{12}{4}\\A=8-3\\A=5$

Answer

5 bags of Vigoro Ultra Turf and 2 of Parker's Premium Starter are needed