Rocks 2

A garden center has one type of rock that sells for $6.50 per cubic yard and another type of rock that sells for $12.80 per cubic yard. They want to make 25.2 cubic yards of a mixture of rock that sells for $12.40/cubic yard. How much of each rock will they need to obtain the desired mixture?

Correct answer:

a =  1.6 yd³
b =  23.6 yd³

Step-by-step explanation:

$$\begin{gathered} 6.5a+12.8b=12.4\cdot (a+b) \\ a+b=25.2 \\ 6.5\cdot a+12.8\cdot b=12.4\cdot (a+b) \\ a+b=25.2 \\ 5.9a-0.4b=0 \\ a+b=25.2 \\ Row2-\frac{1}{5.9}\cdot Row1\to Row2 \\ 5.9a-0.4b=0 \\ 1.07b=25.2 \\ b=\frac{25.2}{1.06779661}=23.6 \\ a=\frac{0+0.4b}{5.9}=\frac{0+0.4\cdot 23.6}{5.9}=1.6=1.6{\text{yd}}^3 \\ a=\frac{8}{5}=1.6 \\ b=\frac{118}{5}=23.6 \end{gathered}$$

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