Fertilizer mixture

A fruit company uses two types of fertilizers in an orange grove, 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. The 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?

Correct answer:

a =  41
b =  56

Step-by-step explanation:

$$\begin{gathered} 8a+7b=720 \\ 4a+6b=500 \\ 8\cdot a+7\cdot b=720 \\ 4\cdot a+6\cdot b=500 \\ 8a+7b=720 \\ 4a+6b=500 \\ Row2-\frac{4}{8}\cdot Row1\to Row2 \\ 8a+7b=720 \\ 2.5b=140 \\ b=\frac{140}{2.5}=56 \\ a=\frac{720-7b}{8}=\frac{720-7\cdot 56}{8}=41 \\ a=41 \\ b=56 \end{gathered}$$

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