Question

BRAINLIETS FOR ANYONE WHO ANSWERS 1ST... I'M DESPARATE

Kendra is making cookies. The recipe calls for `6\ \frac{3}{4}` cups flour for 4 batches of cookies. Janel is using the same recipe. She will make b batches of cookies using c cups of flour. Write two equations that represent the relationship between b and c.

Use the table to help guide you. The table will not be provided on the test, so you will need to decide whether to create your own table or not to help you with this problem.

Hints: When you solve for 1 cup of flour in the table, the number of batches you get, b, is the constant of proportionality. If you know the constant of proportionality, then you should be able to write an equation. As tempting as it is to use the calculator on this problem, it will actually be easier if you use fractions.

b = ___________ c

You can then write a second equation by reversing the variables and using the reciprocal.

c = ___________ b

Answer 1

1) The first equation is;

b =
`0.\overline {592}` × c

2) The second equation is;

c = 1.6875 × b

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 =
`6 (3)/(4) \ cups= (27)/(4) \ cups`

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 =
`0.\overline {592}`

Therefore, the first equation is given as follows;

b = 16/27 × c

∴ b =
`0.\overline {592}` × 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