Question

you have one type of chocolate that sells for $5.00/lb and another type of chocolate that sells for $9.60/lb. you would like to have 27.6 lbs of a chocolate mixture that sells for $6.00/lb. how much of each chocolate will you need to obtain the desired mixture?

Answer 1

To obtain the desired mixture, you will need 21.4 lbs of the first type of chocolate and 6.2 lbs of the second type of chocolate.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's represent the amount of the first type of chocolate as x and the amount of the second type of chocolate as y. Since we want to have a total of 27.6 lbs of chocolate mixture, we can write the equation x + y = 27.6.

We also know that the cost per pound of the mixture is $6.00, so we can write the equation (5x + 9.60y)/27.6 = 6.00. Now we can solve this system of equations to find the values of x and y.

First, let's rearrange the first equation to solve for x: x = 27.6 - y. Now substitute this expression for x in the second equation: (5(27.6 - y) + 9.60y)/27.6 = 6.00. Simplifying this equation gives us 138 - 5y + 9.60y = 166.56. Combining like terms, we get 4.6y = 28.56. Dividing both sides by 4.6 gives us y = 6.2. Substitute this value of y back into the first equation to solve for x: x = 27.6 - 6.2 = 21.4.

Therefore, you will need 21.4 lbs of the first type of chocolate and 6.2 lbs of the second type of chocolate to obtain the desired mixture.