homework plsssss

Question

One gram of protein contains 4 calories. One gram of fat contains 9 calories. A snack has 60 calories from p grams of protein and f grams of fat.

The equation 4p+9f=60 represents the relationship between these quantities.

Determine if each pair of values could be the number of grams of protein and fat in the snack. Be prepared to explain  your reasoning.

8.If there are 6 grams of fat in the snack, how many grams of protein are there? Show your reasoning.

9.In this situation, what does a solution to the equation 4p+9f=60 tell us? Give an example of a solution.

Answer 1

4p+9f = 60

if f=6, then 4p=60-9(6) = 60-54 = 6 and p =6/4 =3/2 = 1.5 = 1 1/2 grams of protein

other possible combinations are

(p, f) = (3/2, 6)

or (p,f) = (3, 16/3)

or (p, f) = (4, 44/9)

or (p, f) = (0, 20/3) = (0, 6 2/3)

or (p, f) = (15, 0)

graph p on the x axis, f on the y axis

plot those last two points (the x and y intercepts) and connect them with a downward sloping straight line. any point on that line is a solution to the equation