Question

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?

Answer 1

`("ganola")/("dried fruit") = 3/2`

Explanation:

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

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

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

and at `($1.75)/("lb")`

would sell for a total of `(1.75) * (g+f)`
or `7/4 * (g+f)` dollars.

So
`color(white)("XXXX")` `5/4*(g+2f) = 7/4(g+f)`

`rArr` `color(white)("XXXX")` `5g + 10f = 7g+7f`

`rArr` `color(white)("XXXX")` `3f = 2g`

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