A health food store sells trail mix made with granola and dried fruit. The store buys granola at $1.00/lb and dried fruit at $2.00/lb, and it sells these items at 25% markup. If the trail mix sells for $1.75/lb, what is the recipe for trail mix?

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A health food store sells trail mix made with granola and dried fruit. The store buys granola at $1.00/lb and dried fruit at $2.00/lb, and it sells these items at 25% markup. If the trail mix sells for $1.75/lb, what is the recipe for trail mix?

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Answer 1 · 2015-08-09T23:53:52

$\frac{ganola}{dried fruit} = \frac{3}{2}$ $("ganola")/("dried fruit") = 3/2$

Explanation:

Suppose a batch of trail mix is made with
$XXXX$ $color(white)("XXXX")$ $g$ $g$ lb of granola and
$XXXX$ $color(white)("XXXX")$ $f$ $f$ lb of dried fruit
Then the cost to make a batch would be
$XXXX$ $color(white)("XXXX")$ $1 \cdot g + 2 \cdot f = g + 2 f$ $1*g + 2*f = g+2f$

With a markup of $25 %$ $25%$ the selling price would be
$XXXX$ $color(white)("XXXX")$ $125 %$ $125%$ or $\frac{5}{4}$ $5/4$ of the cost.

A batch weights
$XXXX$ $color(white)("XXXX")$ $g + f$ $g+f$ lb

and at $\frac{$ 1.75}{lb}$ $($1.75)/("lb")$

would sell for a total of $(1.75) \cdot (g + f)$ $(1.75) * (g+f)$
or $\frac{7}{4} \cdot (g + f)$ $7/4 * (g+f)$ dollars.

So
$XXXX$ $color(white)("XXXX")$ $\frac{5}{4} \cdot (g + 2 f) = \frac{7}{4} (g + f)$ $5/4*(g+2f) = 7/4(g+f)$

$\Rightarrow$ $rArr$ $XXXX$ $color(white)("XXXX")$ $5 g + 10 f = 7 g + 7 f$ $5g + 10f = 7g+7f$

$\Rightarrow$ $rArr$ $XXXX$ $color(white)("XXXX")$ $3 f = 2 g$ $3f = 2g$

That is the ratio of dried fruit to granola is $2 : 3$ $2:3$

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A health food store sells trail mix made with granola and dried fruit. The store buys granola at $1.00/lb and dried fruit at $2.00/lb, and it sells these items at 25% markup. If the trail mix sells for $1.75/lb, what is the recipe for trail mix?

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Explanation:

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