Question

You have one type of chocolate that sells for $2.40/lb and another type of chocolate that sells for $9.90/lb. You would like to have 30 lbs of a chocolate mixture that sells for $4.20/lb. How much of each chocolate will you need to obtain the desired mixture

Answer 1

We need 22.8 lbs of the first type of chocolate and 7.2 lbs of the second type of chocolate

Explanation:

Step 1 :

Let x represent the quantity of the first type of chocolate

and y represent the quantity of the second type of chocolate

The quantity of the final mixture required = 30 lbs

Hence

x + y = 30

Step 2 :

Price of the first type of chocolate = $ 2.40 / lb

Price of the second type of chocolate = $9.90/lb

The total price of the final mixture = $4.20 / lb

Hence the price for 30 lbs = 4.2 × 30 = $126

Hence the equation representing this would be

2.4 x + 9.9 y = 126

Step 3 :

Solving the equations obtained in step 1 and 2 for x and y we get,

2.4 x + 2.4 y = 72

2.4 x + 9.9 y = 126

Subtracting equation 2 from 1 we get,

-7.5 y = -54 = > y = 7.2

x + y = 30 = > x = 30 - y = 30 - 7.2 = 22.8

Step 4 :

Answer :

We need 22.8 lbs of the first type of chocolate and 7.2 lbs of the second type of chocolate