students are responsible for providing snacks and drinks for the junior Bear club induction reception. Susan and Myra or asked to provide the punch for the 100 students and family members who will attend the event. the chart below will help Susan and Myra determine the proportion of cranberry juice to sparkling water needed to make the punch. complete the chart, graph the data, and write the equation that models this proportional relationship.

The proportional relationship between the cranberry Juice and the number of cups of sparkling water required to make a punch is [tex] C = \frac {4}{5}S[/tex] ; where C is the amount of cranberry juice and S is the number of cups of sparkling water.

The completed value table :

Sparkling water, S __ Cranberry Juice, C
1 _________________ [tex] \frac{4}{5} [/tex]
5 _________________ [tex] 4 [/tex]
8 _________________ [tex] 6 \frac{2}{5} [/tex]
12 ________________ [tex] 9 \frac{3}{5} [/tex]
50 ________________[tex] 40 [/tex]
100 _______________ [tex] 80 [/tex]

The proportional relationship between proportion of cranberry juice to sparkling water required to make a punch can be expressed thus :

Let :

Cranberry juice = C
Sparkling water = S

Hence,

C α S

C = kS

Where, k = constant of proportionality ;

We can obtain the value of k when, s = 5 and c = 4

Substitute the values into the equation :

4 = 5k

Divide both sides by 5

k = [tex] \frac {4}{5} [/tex]

Hence, the relationship between Cranberry Juice and number of cups of Sparkling water is : [tex] C = \frac {4}{5}S[/tex]

When, S = 1 ;

[tex] C = \frac{4}{5} \times 1 = \frac{4}{5} [/tex]

When, S = 50

[tex] C = \frac{4}{5} \times 50 = 40 [/tex]

THEREFORE, the proportionality constant between proportion of Cranberry Juice and number of cups of Sparkling water is [tex] \frac{4}{5} [/tex]

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