Rafael buys apples from the local orchard. The table below shows the relationship between the cost C (in dollars) and the weight W (in kilograms) of the apples purchased.
Weight
(kilograms)
Cost
(dollars)
(a)For the information in the table, write an equation to represent the relationship between C and W.
(b)Choose the correct statement to represent this relationship.
Apples cost 4 dollars per kilogram.
Apples cost 1 dollar per 4 kilograms.
Apples cost 16 dollars per kilogram.
Apples cost 1 dollar per kilogram.
(a) The equation to represent the relationship between C (cost in dollars) and W (weight in kilograms) can be written as:
C = kW
where k represents the cost per kilogram.
(b) The correct statement to represent this relationship is: Apples cost 1 dollar per kilogram.
(a) To write an equation representing the relationship between the cost C (in dollars) and weight W (in kilograms) of the apples purchased, we can set up a linear equation in slope-intercept form.
Let's assume the equation is given by:
C = mW + b,
where m represents the rate (slope) at which the cost changes with weight, and b represents the initial cost (y-intercept).
To find the values of m and b, we can take two points from the table and substitute their values into the equation. Let's use the points (2, 8) and (4, 16) from the table:
Using the point (2, 8):
8 = 2m + b, (1),
Using the point (4, 16):
16 = 4m + b. (2).
To solve this system of linear equations, we can subtract equation (1) from equation (2):
16 - 8 = 4m + b - (2m + b),
8 = 2m.
Simplifying, we get:
2m = 8,
m = 4.
Now, substituting the value of m into equation (1), we can solve for b:
8 = 2(4) + b,
8 = 8 + b,
b = 0.
Therefore, the equation representing the relationship between C and W is:
C = 4W.
(b) The correct statement to represent this relationship is: Apples cost 4 dollars per kilogram.
(a) To write an equation representing the relationship between the cost C (in dollars) and the weight W (in kilograms) of the apples purchased, we need to determine the pattern or ratio between the two variables. Looking at the table, we observe that the cost increases as the weight increases.
One way to find the equation is to calculate the slope of the line connecting two points from the table. Let's take the points (2, 8) and (5, 20) from the table:
Slope (m) = (change in y)/(change in x) = (20 - 8)/(5 - 2) = 12/3 = 4.
Therefore, the equation representing the relationship between C and W is: C = 4W.
(b) Looking at the equation C = 4W, we can see that the correct statement to represent this relationship is: Apples cost 4 dollars per kilogram.