Answer :
Final answer:
To determine the number of bags of each type of fertilizer required to yield a mixture containing specific amounts of nitrogen, phosphoric acid, and potash, a system of equations can be set up and solved. The equations represent the amounts of each nutrient in each type of fertilizer, and the desired amounts in the mixture. Solving the system will give the number of bags of each type of fertilizer required.
Explanation:
To determine the number of bags of each type of fertilizer required to yield a mixture containing 181 pounds of nitrogen, 65 pounds of phosphoric acid, and 32 pounds of potash, we can set up a system of equations.
Let x represent the number of bags of Vigoro Ultra Turf fertilizer, and y represent the number of bags of Parker's Premium Starter fertilizer.
We can write the following equations:
29x + 18y = 181 (for nitrogen)
3x + 25y = 65 (for phosphoric acid)
4x + 6y = 32 (for potash)
Solving this system of equations will give us the values of x and y, which represent the number of bags of each type of fertilizer required.
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:
[tex]29A+18B=181\\3A+25B=65\\4A+6B=32[/tex]
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:
[tex]1) 3A+25B=65\\2) 4A+6B=32[/tex]
One incognita is cleared depending on the other
[tex]2) 4A+6B=32\\4A=32-6B\\A=8-\frac{6}{4} B[/tex]
The values obtained in the second are replaced
[tex]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[/tex]
With the value of B it is replaced in the first one to obtain the value of A:
[tex]A=8-\frac{6}{4} B\\A=8-\frac{12}{4}\\A=8-3\\A=5[/tex]
Answer
5 bags of Vigoro Ultra Turf and 2 of Parker's Premium Starter are needed
