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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