Question

You need 3 1/2 cups of flour for each batch of cupcakes. How many whole batches can make if you have 17 cups of flour? Show two ways.

Answer 1

4 batches of cupcakes can be made.

SOLUTION:

Given, we need
`3(1)/(2)` cups of flour for each batch of cupcakes. And we have 17 cups of flour.

We need to find how many batches can be made.

1st way:

We will get the number of batches when we divide the available cups with cups required for one batch.

Available cups = 17 and required cups for one batch =
`3(1)/(2)` =
`(7)/(2)` cups

number of batches =
`$(17)/((7)/(2))$`

`$=(17)/(1) * (2)/(7)$`

`$=(34)/(7)$` = 4.857

As the number of batches can’t be fraction, we will neglect the fractional part.

2nd way:

Let the number of batches be x.

Then, cups of flour required for batches must be less than available flour

(x)(
`(7)/(2)`) < 17

(x)(7) < (2)(17)

7x < 34

x <
`(34)/(7)`

x < 4.857

As the number of batches must be an whole number, x becomes 4.

Hence, 4 batches of cupcakes can be made.