20 pounds of cocoa and 13 pounds of sugar

Question

At one stage in a factory’s candy production, cocoa is mixed with sugar. For every

20 pounds of cocoa, 13 pounds of sugar are needed.

1. Describe a function that arises from this situation
2. Make a table and draw the graph of your function.
3. Find an equation for your function and explain why your equation is valid.

Answer 1

C/S= 20/13

the ratio of cocoa to sugar is a constant

S= 13C/20 or C = 20S/13

S(C) = (13/20)C or C(S) = (20/13)S

S(C) = 0.65C

or S/(C+S) = 13/(20+13) = 13/33

and C/(C+S) = 20/(20+13)= 20/33

S(T) =(13/33)T where T is the total amount needed

C(T) = (20/33)T Cocoa is about 60% of the Total mixture, Sugar = about 40% of the Total mixture

the graph is a straight line through the origin, upward sloping