Question
A hardware store mixes a $6 per pound nut mix with a $9 per pound nut mix to create a 30-pound mix that sells for $7 per pound. How many pounds of each type of nut mix are used?
A hardware store mixes a $6 per pound nut mix with a $9 per pound nut mix to create a 30-pound mix that sells for $7 per pound. How many pounds of each type of nut mix are used?
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Koala Tutor
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Let $x$ be the number of pounds of the $6 per pound nut mix used.
Thus, there are $30-x$ pounds of the $9 per pound nut mix used.
So, we have the equation $6x+9(30-x)=7\cdot30$.
Or, simplifying the equation to $6x+270-9x=210$,
we have $-3x=-60$, or $x=20$.
Thus, the number of pounds of the $6 per pound nut mix used is $\boxed{20}$, and the number of pounds of the $9 per pound nut mix used would be $30-20=\boxed{10}$.
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