pounds of mixed nuts worth $$ 4.75 /lb$ should be combined with $10 lb$ of dried fruits worth $$ 5.50 /lb$ to make a trail mix that would sell for $$ 4.95 /lb$ .

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Solution

Let the required amount of mixed nuts be $n$ pounds.

Here, the price of trail mix, which is $$ 4.95 /lb$ , is the weighted average of the price of $n$ lb mixed nuts and $10$ lb dried fruits.

$∴ $ 4.95 /lb = \frac{(n \times 4.75) + (10 \times 5.50)}{(n + 10)}$

$\Rightarrow 4.95 \times (n + 10) = \frac{(n \times 4.75) + (10 \times 5.50)}{(n + 10)} \times (n + 10)$

$\Rightarrow 4.95 n + 49.5 = 4.75 n + 55$

$\Rightarrow 4.95 n + 49.5 - 4.75 n - 49.5 = 4.75 n + 55 - 4.75 n - 49.5$

$\Rightarrow (4.95 - 4.75) n = 55 - 49.5$

$\Rightarrow 0.20 n = 5.5$

$\Rightarrow 2 n = 55$
(Multiplying both sides of the equation by $10$ )

$\Rightarrow n = \frac{55}{2} = 27.5$
(Dividing both sides of the equation by $2$ )

$∴$ $27.5 pounds - ------------ -$ of mixed nuts worth $$ 4.75 /lb$ should be combined with $10 lb$ of dried fruits worth $$ 5.50 /lb$ to make a trail mix that would sell for $$ 4.95 /lb$ .

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