Question

Use the information in the 1st question to help you out in questions 2 and 3

Answer 1

Problem One
There is nothing wrong with the answer you got.

Gives and required.
1 batch of cookies requires 1/3 cup of sugar
x batches of cookies will need 5 cups of sugar.

Proportion
1 / x = 1/3 / 5

Solve
You could change 1/3 into 0.33333333
1/x= 0.33333333/5 Cross multiply
5 * 1 = 0.333333x
5 = 0.33333333x Divide by 0.3333333
x = 5/0.33333333
x = 15 <<<<< Answer

Problem 2
Givens
9 cups of sugar

Proportion
1 batch requires 1/3 cup of sugar
x batches will require 9 cups of sugar.

1/x = 1/3 //9
1/x = 0.3333333 / 9 Cross multiply
9*1 = 0.3333333 x
9 = 0.33333333x Divide by 0.33333333
9/0.33333333 = x
x = 27 batches of cookies. <<< Answer

Ignore the very small decimal you get. It does not matter. It is a rounding error.

Problem 3
Let the whole shift = x
Let the shift Fred signed up for = x/2

Now x/2 has to be split 3 ways. How do we do that?

Well we can represent it.


`( (x)/(2) )/(3)`

The best way to proceed is to put a 1 under the three.


`((x)/(2))/((3)/(1) )`

Now you get to invert the bottom fraction (3/1) so that it becomes (1/3) and multiply the two fractions together.


`(x)/(2) * (1)/(3)=(x*1)/(2*3)= (x)/(6)`

Answer: Each friend will work 1/6 of a whole shift.