College Algebra, Chapter 1, 1.2, Section 1.2, Problem 52

Suppose that a merchant blends tea that sells for $\$ 3.00$ a pound with tea that sells for $\$ 2.75$ a pound to produce $80$ lb of a mixture that sells for $\$ 2.90$ a pound. How many pounds of each type of tea does the merchant use in the blend?










$
\begin{equation}
\begin{aligned}

3(x) + 2.75(80 - x) =& 2.90(80)
&& \text{Model}
\\
\\
3x + 220 - 2.75x =& 232
&& \text{Solve for } x
\\
\\
0.25 x =& 12
&&
\\
\\
x =& 48
&&

\end{aligned}
\end{equation}
$


In order to produce an $80$ lb of a mixture that sells $\$ 2.90$ per lb, the merchant should blend a $48$ lb of mixture that sells $\$3$ per lb in a $32$ lb of mixture that sells $\$2.75$ per lb.

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