# A mixture of 30 pounds of candy sells for $1.10 a pound. The mixture consists of chocolates worth $1.50 a pound and chocolates worth 90 cents a pound. How many pounds of the $1.50 chocolate were used to make the mixture?

##### 2 Answers

10 lbs of the more expensive chocolate was used.

#### Explanation:

Let

Based on total pounds we know:

Based on cost we know

We can simplify the cost equation:

cross multiply:

distribute:

move everything to one side:

Now we can solve the system:

From the first equation we know that

Substituting into

expanding:

collecting:

subtract 12 from both sides:

divide through by

Taking

Since

This is a simultaneous equation problem.

Chocolate used at $1.50 per pound is 10 pounds

Chocolate used at $0.90 per pound is 20 pounds

#### Explanation:

Let the weight of chocolates worth $0.90 a pound be

Let the weight of chocolates worth $1.50 a pound be

Initial conditions:

The value of the blend is

Thus we have:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

You may choose which one you so wish to substitute for. I choose

Consider

Write as

Using

Dropping the units of measerment for now.

Subtract 26 from both sides

Divide both sides by