Claire works at the Sweet Shop, where candy is bagged and sold by its weight. Claire's last 4 sales of gourmet gummy worms are shown in the table.
The cost of the gummy worms is proportional to the amount, in pounds, of gummy worms purchased.
This situation can be represented by an equation in the form y = kx, where k is the constant of proportionality.
Gourmet
Gummy Worms,
x (pounds)
Cost,
y
0.75 $6.30
2.5 $21.00
4 $33.60
7 $58.80
What is the constant of proportionality?
Responses
A $4.73$4.73
B $14.70$14.70
C $8.40$8.40
D $8.30
B $14.70
To find the constant of proportionality (k), we can use any two sets of x and y values. Let's use the first two sets: (0.75, $6.30) and (2.5, $21.00).
Using the formula y = kx, we can set up the following two equations:
6.30 = 0.75k
21.00 = 2.5k
Solving the first equation for k:
k = 6.30 / 0.75
k = 8.4
Now, we can verify our result by using the second set of values:
21.00 = 2.5 * 8.4
21.00 = 21.00
Since the equation holds true, k = $8.40. So, the constant of proportionality is $8.40.