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. Juanita 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 = 30Assuming Juanita used the information given and her other knowledge of the candies, use her equations to answer the following:a) How many pounds of candy are in the box?b) What is the price per pound of the caramels?c) What does the term 12y in the second equation represent?d) What does 8x+12y+1 in the second equation represent?

Answer 1

a)From the information given, x is the number of pounds of caramels included in the box and y is the number of pounds of truffles in the box. The given equations are

x + y = 3

8x + 12y + 1 = 30

The pounds of candy in the box is x + y = 3. Thus, there are 3 pounds of candy in the box.

b) Since x represents the number of pounds of caramels and equation 2 represents total cost, then, the price per pound of caramels is $8

c) 12y represents the the cost of y pounds of truffles.

d) 8x + 12y + 1 in the second equation represents

Cost of x pounds of caramels + cost of y pounds of truffles + cost of box = $30