Carrie’s Chocolate Shop and Tamika’s Treat Shop both sell candy in boxes. The table below lists the price (the total amount the customer pays) of each box of candy sold at the shops. For each shop, there is a linear relationship between the price of a box of candies and the number of candies in that box. These are the only numbers of candies that can be purchased at the shops.
1. Jeremy has $10.00 in quarters to spend on candy. What is the maximum number of quarters he would have left after paying for a box of 25 candies at Tamika’s Treat Shop (Note: Each quarter is worth $0.25.)
2. At Tamika’s Treat Shop, what is the average price per candy in a box of 20, to the nearest $0.01 ?
3. Which of the following equations gives the relationship between the price in dollars, c, and the number of candies, n, in a box of candies at Carrie’s Chocolate Shop?
1. The correct answer is D.
Amount left = $10.00 - $4.25 = $5.75
And $5.75 = 23 × $0.25 quarters.
2. The correct answer is B.
The average price per candy is the total price divided by the number of candies. This is equal to $3.75/20 = $0.1875 or $0.19 when rounded to the nearest $0.01.
3. The correct answer is A.
You can verify that the relationship is linear by noting that each increase of 5 candies results in an increase of $1.00 in price so that the slope of the line is
m = 1.00/5 = 0.20
The equation can then be written in the form c = 0.2n + b
You can solve for the value of b by substituting any one of the (n, c) ordered pairs for Carrie’s Chocolate Shop into the equation.
Using (5, 1.50), we have b = 1.50 - 0.20(5) = 0.50
Therefore, the correct equation is c = 0.20n + 0.50