Question

A baker used a recipe to make cookies. He used 8 3/4 cups of flour to make 2 1/2 times the original recipe. How many cups of flour are needed in the original recipe? Show you work or explain your reasoning

Answer 1

`(7)/(2)` cups of flour are needed in the original recipe

Solution:

Given that, Baker used
`8(3)/(4)` cups of flour to make
`2(1)/(2)` times the original recipe

To find: Cups of flour are needed in the original recipe

Let the cups of flour in original recipe be "x"

From given statement, we can frame a equation as:

Cups of floor used =
`2(1)/(2)` times the original recipe

`8(3)/(4) = 2(1)/(2) \text{ times the } x`

Here "times" means multiplication or product

`8(3)/(4) = 2(1)/(2) * x\\\\(4 * 8 +3)/(4) = (2 * 2+1)/(2) * x\\\\(35)/(4) = (5)/(2) * x\\\\35 = 10x\\\\x = (35)/(10) = (7)/(2)`

Thus
`(7)/(2)` cups of flour are needed in the original recipe

Show you work or explain your reasoning

Multiply the original recipe cups by
`2(1)/(2)` to get
`8(3)/(4)`

`(7)/(2) * 2(1)/(2) = 8(3)/(4)\\\\(7)/(2) * (5)/(2) = (35)/(4)\\\\(35)/(4) = (35)/(4)`

Thus answer is correct