Question

A candy shop sells a box of chocolates for $30. It has $29 worth of chocolates plus $1 for the box. The box includes two kinds of candy: caramels and truffles. Lita knows how much the different types of candies cost per pound and how many pounds are in a box. She said,

If x is the number of pounds of caramels included in the box and y is the number of pounds of truffles in the box, then I can write the following equations based on what I know about one of these boxes:

x + y = 3
8x + 12y + 1 = 30

Assuming Lita used the information given and her other knowledge of the candies, use her equations to answer the following:

How many pounds of candy are in the box?

What is the price per pound of the caramels

What does the term 12y in the second equation represent?

What does 8x + 12y + 1 in the second equation represent?

Answer 1

There are 3 lbs of candy in the box.

The caramels are $8 per pound.

12y represents the total cost of truffles in the box.

8x + 12y + 1 represents the cost of caramels in the box + the cost of truffles in the box + the cost of the box.

Explanation:

x = the number of pounds of caramels

y = the number of pounds of truffles

x + y = total lbs. and we know x + y = 3

We know x is the number of pounds of caramels.

8x = (cost per pound of caramels) × (number of pounds of caramels)

So 8 = cost of caramels

We know y = number of pounds of truffles. So 12 is the cost of truffles by pound, and 12y is the total cost of truffles in the box.

Based on all the above,

The cost of caramels in the box + the cost of truffles in the box + the cost of the box is = total cost of the box. 8x + 12y + 1 = 30