One recipe for cereal bars uses 5 cups of cereal and 2 1/2 cups of nuts. A different recipe uses 3 cups of cereal and 1 cup of nuts. Which recipe is more nutty? Please show work.

The first recipe is nuttier than the second recipe.

Step-by-step explanation:

Step 1:

The first recipe uses 5 cups of cereal and cups of nuts while the second recipe uses 3 cups of cereal and 1 cup of nuts.

To determine which recipe is nuttier, we convert the two recipes to the same scale.

The first recipe uses 5 cups of cereal while the second recipe uses 3 cups of cereal.

The number 15 is the least common multiple of 5 and 3.

Step 2:

In order to convert 5 cups to 15 cups, we multiply 5 by 3 so 15 cups of cereal have cups of nuts i.e. .

In order to convert 3 cups to 15 cups, we multiply 3 by 5 so 15 cups of cereal have cups of nuts.

So for 15 cups of cereal, the first recipe has 12.5 cups of nuts while the other recipe has 5 cups of nuts.

So the first recipe is nuttier than the second recipe.

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!