Answer:
1) The first equation is;
b = [tex]0.\overline {592}[/tex] × c
2) The second equation is;
c = 1.6875 × b
Step-by-step explanation:
In making cookies the recipe Kendra uses to produce a given number of batches of cookies are;
The number of cups of flour, c = [tex]6 \dfrac{3}{4} \ cups= \dfrac{27}{4} \ cups[/tex]
The number of batches of cookies made, b = 4 batches
1) The the constant of proportionality that relates 'b', the number of batches of cookies and 'c', the number of cups of flours required is given by finding the number of cookie batches we get from 1 cup of flour as follows;
We can write;
4 batches of cookies, b ∝ 27/4 cups of flour, c
b ∝ c
4 batches of cookies, b = (27/4 cups of flour, c) × k
b = c × k
∴ b = k × c (by commutative property of multiplication)
Where;
k = The constant of proportionality
K is given by dividing both sides of the equation by (27/4 cups of flour) as follows;
(4 batches of cookies)/(27/4 cups of flour)= ((27/4 cups of flour) × k)/(27/4 cups of flour)
∴ k = 16/27 cups of flour per batch of cookie
16/27 = [tex]0.\overline {592}[/tex]
Therefore, the first equation is given as follows;
b = 16/27 × c
∴ b = [tex]0.\overline {592}[/tex] × c
2) The second equation is found by dividing both sides by 16/27 as follows;
b = 16/27 × c
b/(16/27) = 16/27 × c/(16/27)
16/27 × c/(16/27) = c
b/(16/27) = 27/16 × b
b/(16/27) = 27/16 × b = (16/27 × c/(16/27)) = c
27/16 × b = c
∴ c = 27/16 × b
27/16 = 1.6875
Therefore, the second equation is given as follows;
c = 27/16 × b
∴ c = 1.6875 × b
