Question

A store owner wants to develop a new snack mix by mixing chocolate and trail mix. How many pounds of chocolate costing $17.60 per pound should be mixed with 23 pounds of trail mix costing $3.70 per pound to create a mixture worth $8.47 per pound.

Answer 1

Let x = pounds of chocolate we need to find.

17.60x + 23(3.70) = 8.47(x + 23)

Solve for x to find your answer.

Answer 2

2.12 pounds

Explanation:

We can write an expression relating the cost of chocolate and trail mix to the total cost of the mixture. Let x by the number of pounds of chocolate needed:

We know the total cost is $8.47. We know that the price of the chocolate per pounds is:

`17.60/x`

and the total price of the trail mix per pound is:

`=3.7/23=0.16`

Therefore the expression must be writen per pound mixture:

`8.47=17.60/x+0.16`

We can solve x by multiplying by x:

`8.47\cdot{x}=17.60+0.16\cdot{x}`

Solve for x:

`8.47\cdot{x}-0.16\cdot{x}=17.60`

`8.31\cdot{x}=17.60`

`x=17.60/8.31=2.12`