A painter mixes cans of green and white paint to make the shade needed for painting a bedroom. The table shows the ratios he can use for the color he wants.
Green cans (y) 6 10 16 18
White cans (x) 9 15 24 27
Which is an equation for the constant of proportionality for this relationship?
A
k = 23k\ =\ \frac{2}{3}k =
3
2
B
k = 32k\ =\ \frac{3}{2}k =
2
3
C
k = 910k\ =\ \frac{9}{10}k =
10
9
D
k = 109k\ =\ \frac{10}{9}k =
9
10
To find the constant of proportionality for this relationship, we need to determine the ratio between the number of green cans and the number of white cans for each option given. The constant of proportionality is the value that when multiplied by the number of white cans will give you the corresponding number of green cans.
Let's go through each option and calculate the ratios:
A) k = 23
To find the ratio, we divide the green cans (y) by the white cans (x) for each option:
Ratio = y / x
Ratio = 6 / 9 = 2/3
Ratio = 10 / 15 = 2/3
Ratio = 16 / 24 = 2/3
Ratio = 18 / 27 = 2/3
B) k = 32
Ratio = y / x
Ratio = 6 / 9 = 2/3
Ratio = 10 / 15 = 2/3
Ratio = 16 / 24 = 2/3
Ratio = 18 / 27 = 2/3
C) k = 910
Ratio = y / x
Ratio = 6 / 9 = 2/3
Ratio = 10 / 15 = 2/3
Ratio = 16 / 24 = 2/3
Ratio = 18 / 27 = 2/3
D) k = 109
Ratio = y / x
Ratio = 6 / 9 = 2/3
Ratio = 10 / 15 = 2/3
Ratio = 16 / 24 = 2/3
Ratio = 18 / 27 = 2/3
From our calculations, we can see that in all the options, the ratio between the number of green cans and white cans is 2/3. Therefore, the equation for the constant of proportionality for this relationship is:
k = 2/3
So the correct answer is (A) k = 23