Question

How much caramel candies at $1.16 a pound should be mixed with lollipops worth 86¢ a pound in order to obtain a mixture of 60 pounds of candy worth a dollar a pound?

Answer 1

Answer:

28 pounds of caramel candies

32 pounds of lollipops.

Step-by-step explanation:

Let x represent pounds of caramel candies and y represent pounds of lollipops.

We are told that the mixture contains 60 pounds of both. We can represent this information in an equation as:

$x+y=60...(1)$

We have been given that caramel candies costs $1.16 per pound, so cost of x pounds would be $1.16x$.

Each pound of lollipop worth 86¢ ($0.86), so cost of y pounds would be $0.86y$.

We are asked to obtain a mixture of 60 pounds of candy worth a dollar a pound. We can represent this information in an equation as:

$1.16x+0.86y=60(1)...(2)$

From equation (1), we will get:

$y=60-x$

Upon substituting this value in equation (2), we will get:

$1.16x+0.86(60-x)=60$

$1.16x+51.6-0.86x=60$

$0.30x+51.6=60$

$0.30x+51.6-51.6=60-51.6$

$0.30x=8.4$

$\frac{0.30x}{0.30}=\frac{8.4}{0.30}$

$x=28$

Therefore, 28 pounds of caramel candies at $1.16 a pound should be mixed with lollipops.

Upon substituting $x=28$ in equation (1), we will get:

$28+y=60$

$28-28+y=60-28$

$y=32$

Therefore, 32 pounds of lollipops should be mixed to obtain the required mixture.