Question

Your doctor says that you should take in at least 150 grams of protein a day.Each slice of salami you put on your sandwich has 15 grams and each scoop youput into your protein shake has 30 grams. Write the system of inequalities thatrepresents the number of salami slices and number of scoops of protein in orderto reach your minimum amount of protein needed.

Answer 1

The protein needed per day is at least 150 grams This means it can be larger than or equal to 150 grams per day .

Protein nedded >= 150 grams

`\text{protein}\ge150`

Now, we need to include for the nutrients that provide that protein:

salami slices = 15 grams per slice

scoop of powder = 30 grams per scoop

Since we don't know the number of slices of salami, we use a letter (s) to represent it.

Since we don't know the number of scoops of protein powder, we use a letter (p) to represent these.

So since per slice we we 15 grams of protein, using "s" slaices we wiould get 15 * s grams of protein (in math terms: "15 s".

Similarly with the scoops of protein powder: If we use "p" scoops, we would get 30 times "p" grams of protein (in math terms: "30 p"

So now we add these two last expression to get the total amount of protein from these sources:

15 s + 30 p

and we want them to provide at least 150 grams of protein. So we write in math terms:

15 s + 30 p >= 150

`15s+30p\ge150`