Question

You have one type of chocolate that sells for $6.00/lb and another type of chocolate that sells for $8.10/lb. You would like to have 12.6 lbs of a chocolate mixture that sells for $7.70/lb. How much of each chocolate will you need to obtain the desired mixture?

Answer 1

• 2.4 pounds of the $6/lb chocolate
• 10.2 pounds of the $8.10/lb chocolate

Work Shown

x = amount, in pounds, of the $6 per pound chocolate

y = amount, in pounds, of the $8.10 per pound chocolate

x+y = total amount of chocolate = 12.6 pounds

x+y = 12.6 solves to y = 12.6 - x

6x = revenue from just the first batch sold

8.10y = revenue from just the second batch

6x+8.10y = total revenue = 12.6*7.70

We end up with the equation 6x+8.10y = 97.02

Let's plug in y = 12.6 - x so we could isolate x.

6x+8.10y = 97.02

6x+8.10(12.6-x) = 97.02

6x+8.10(12.6)+8.10(-x) = 97.02

6x+102.06-8.10x = 97.02

-2.1x+102.06 = 97.02

-2.1x = 97.02-102.06

-2.1x = -5.04

x = -5.04/(-2.1)

x = 2.4

Then,

y = 12.6 - x

y = 12.6 - 2.4

y = 10.2

Answer 2

We need 2.68 lbs of the $6.00/lb chocolate and 9.92 lbs of the $8.10/lb chocolate to obtain 12.6 lbs of a chocolate mixture that sells for $7.70/lb

Explainion:

Let x be the number of pounds of the $6.00/lb chocolate needed, and y be the number of pounds of the $8.10/lb chocolate needed.

We know that the total amount of chocolate needed is 12.6 lbs, so we can write:

x + y = 12.6

We also know that the mixture must sell for $7.70/lb, so we can write:

(6.00)x + (8.10)y = (7.70)(12.6)

Simplifying the second equation by multiplying everything out, we get:

6x + 8.1y = 96.42

Now we have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution:

From the first equation, we can solve for one variable in terms of the other:

x + y = 12.6

y = 12.6 - x

Now we can substitute this expression for y into the second equation:

6x + 8.1y = 96.42

6x + 8.1(12.6 - x) = 96.42

Distributing the 8.1, we get:

6x + 102.06 - 8.1x = 96.42

Simplifying and solving for x, we get:

-2.1x = -5.64

x = 2.68

Now we can use this value of x to solve for y using the first equation:

x + y = 12.6

2.68 + y = 12.6

y = 9.92

Therefore, we need 2.68 lbs of the $6.00/lb chocolate and 9.92 lbs of the $8.10/lb chocolate to obtain 12.6 lbs of a chocolate mixture that sells for $7.70/lb

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