In a proportional relationship, the constant of proportionality is the number you can multiply each value of x by to get the related value of y. You can use this idea to figure out whether a set of values is in a proportional relationship. Divide each value of y by the related value of x. Do you get the same number every time?
In our ice cream example, $2 divided by 1 scoop equals 2. $4 divided by 2 scoops also equals 2. And $6 divided by 3 scoops…you get the picture! The relationship’s proportional, and the constant is 2.
Which of these is a proportional relationship?
A.Justin charges $1 for 1 cup of lemonade, $3 for 2 cups of lemonade and $4 for 3 cups of lemonade.
B. Jared charges $1 for 1 cup of lemonade, $2 for 2 cups of lemonade and $3.50 for 3 cups of lemonade.
C. Jasmyne charges $1 for 2 cups of lemonade, $2 for 4 cups of lemonade and $3 for 6 cups of lemonade.
D. Jessica charges $1 for 1 cup of lemonade and $2 for anyone who wants 2, 3 or 4 cups of lemonade.
The answer is A. Justin charges $1 for 1 cup of lemonade, $3 for 2 cups of lemonade, and $4 for 3 cups of lemonade.
To determine which of these options represents a proportional relationship, we need to check if the ratio between the values of y and x is the same every time. Let's analyze each option:
A. Justin charges $1 for 1 cup of lemonade, $3 for 2 cups, and $4 for 3 cups. The ratio of cost to the number of cups is 1/1, 3/2, and 4/3. These ratios are not the same, so option A does not represent a proportional relationship.
B. Jared charges $1 for 1 cup of lemonade, $2 for 2 cups, and $3.50 for 3 cups. The ratio of cost to the number of cups is 1/1, 2/2, and 3.5/3. Again, these ratios are not the same, so option B does not represent a proportional relationship.
C. Jasmyne charges $1 for 2 cups of lemonade, $2 for 4 cups, and $3 for 6 cups. The ratio of cost to the number of cups is 1/2, 2/4, and 3/6. If we simplify these ratios, we get 1/2, 1/2, and 1/2. Since the ratios are the same every time, option C represents a proportional relationship.
D. Jessica charges $1 for 1 cup of lemonade and $2 for anyone who wants 2, 3, or 4 cups of lemonade. This represents a constant price for any number of cups. Therefore, option D also represents a proportional relationship.
Thus, options C and D represent a proportional relationship.
To determine whether a set of values represents a proportional relationship, we can follow the steps mentioned earlier.
Let's apply these steps to the given options:
A. Justin charges $1 for 1 cup of lemonade, $3 for 2 cups of lemonade, and $4 for 3 cups of lemonade.
Justin's prices are not consistent. The second price is three times the first price, but the third price is not four times the first price. Therefore, this set of values does not represent a proportional relationship.
B. Jared charges $1 for 1 cup of lemonade, $2 for 2 cups of lemonade, and $3.50 for 3 cups of lemonade.
Jared's prices are also not consistent. The second price is two times the first price, but the third price is not three and a half times the first price. Therefore, this set of values does not represent a proportional relationship.
C. Jasmyne charges $1 for 2 cups of lemonade, $2 for 4 cups of lemonade, and $3 for 6 cups of lemonade.
Jasmyne's prices are consistent. The second price is two times the first price, and the third price is three times the first price. Therefore, this set of values represents a proportional relationship.
D. Jessica charges $1 for 1 cup of lemonade and $2 for anyone who wants 2, 3, or 4 cups of lemonade.
Jessica's prices are consistent. The second price is two times the first price. Therefore, this set of values represents a proportional relationship.
So, the options that represent a proportional relationship are:
C. Jasmyne charges $1 for 2 cups of lemonade, $2 for 4 cups of lemonade, and $3 for 6 cups of lemonade.
D. Jessica charges $1 for 1 cup of lemonade and $2 for anyone who wants 2, 3, or 4 cups of lemonade.