Question

A fruit company uses two types of fertilizers in an orange groove, brand A and brand B. each bag of brand A contains 8 pounds of nitrogen and 4 pounds of phosphoric acid. Each bag of brand B contains 7 pounds of nitrogen and 6 pounds of phosphoric acid. Test indicates that the groove needs 720 pounds of nitrogen and 500 pounds of phosphoric acid. How many bags of each brand should be used to provide the required amount of nitrogen and phosphoric acid?

Answer 1

for brand A it required 41 bags and for brand B is required 56 bags

Explanation:

The computation is shown below:

Let us assume Brand A be x

And, brand B be y

Now according to the question

The following equations are

8x + 7y = 720

4x + 6y = 500

Multiply by 2 in equation 2

8x + 7y = 720........(1)

8x + 12y = 1000..........(2)

Now subtract equation 1 from equation 2

5y = 280

y = 56 bags

And, x is

8x + 7(56) = 720

8x + 392 = 720

8x = 328

x = 41 bags

hence, for brand A it required 41 bags and for brand B is required 56 bags