To find the price per pound of the Fuji apples, we can divide the total cost by the total weight in pounds of the apples purchased. Crystal bought 3 pounds of apples for [tex]$9.00, so the price per pound can be calculated as follows:
Total cost of apples = $[/tex]9.00
Total weight in pounds = 3 pounds
Price per pound = Total cost / Total weight
Price per pound = [tex]$9.00 / 3 pounds
Price per pound = $[/tex]3.00 per pound
The price per pound is [tex]$3.00.
We want to write an equation that relates the total cost (y) to the weight of the apples in pounds (x). Since the price per pound is constant, the relationship between these variables is linear and directly proportional. Using y for the total cost and x for the weight in pounds, our equation is:
y = (price per pound) × x
Substituting the price per pound, we get:
y = $[/tex]3.00 × x
This equation shows that for every pound of apples Crystal buys, the total cost increases by [tex]$3.00.
In a linear equation such as this one, the slope is the coefficient of x, which represents the rate of change of the total cost with respect to the weight of the apples. In our case, the slope is the price per pound, which is $[/tex]3.00. The slope indicates that for each additional pound of apples bought, the cost increases by [tex]$3.00.
Lastly, this situation is proportional. In a proportional relationship, when one quantity increases, the other quantity increases at a constant rate. Since doubling the weight of apples doubles the cost, tripling the weight triples the cost, and so on, the relationship is directly proportional. This is reflected in the equation y = $[/tex]3.00 × x, which is a linear equation passing through the origin (0,0), another characteristic of proportional relationships.
