Question

One recipe calls for 3 1/2 cups of milk and a second recipe calls for 3 3/4 cups of milk. If you only have 7 cups of milk, can you make both recipes? Why?

Answer 1

To make two separate recipes from the same source means the addition of both must be equal to the source, or at least can be taken from the source with or without a remainder.

What this means is that 7 cups of milk should be able to yield two recipes that requires 3 1/2 cups and 3 3/4 cups (with or without a remainder). If the addition of both exceeds 7 cups of milk then it would not be possible.

This can be expressed mathematically as follows;

`3(1)/(2)+3(3)/(4)\leq7`

If we solve the above inequality, we now have;

`\begin{gathered} (7)/(2)+(15)/(4)\leq7 \\ We\text{ take the LCM of the left side and we now have} \\ (14+15)/(4)\leq7 \\ (29)/(4)\leq7 \\ 7(1)/(4)\leq7 \end{gathered}`

As we can see from the result, both recipes would require 7 1/4 cups of milk which is not less than 7 cups and its also not equal to 7 cups of milk.

Therefore, we cannot make both recipes