Question

How many pounds of butterscotch candy at $2.45 per pound must the Candy Castle mix with caramel candy at a dollar and $1.35 per pound to obtain a 5 pound mixture that sells for a dollar and $1.57 per pound

Answer 1

1 pound of butterscotch candy is mixed with 4 pounds of caramel candy.

Explanation:

Let x be the amount of butterscotch candy and y be the amount of caramel candy in pounds.

Total amount of mixture = 5 pounds

Thus, we can write the equation:

`x+y = 5`

Cost of butterscotch candy = $2.45 per pound

Cost of caramel candy = $1.35 per pound

Cost of mixture = $1.57 per pound

Thus, we can write the equation:

`2.45x +1.35y = 1.57(x+y)\\2.45x +1.35y = =7.85`

Solving the two equation by substitution, we get,

`2.45(5-y) +1.35y = 7.85\\12.25 - 1.1y = 7.85\\\Rightarrow y = 4\\\Rightarrow x = 1`

Thus, 1 pound of butterscotch candy is mixed with 4 pounds of caramel candy.