A nutritionist planning a diet for a football player wants him to consume 3,500 Calories and 725 grams of food daily. Calories from fat and protein will be 45% of the total Calories. There are 4, 4, and 9 Calories per gram for protein, carbohydrates, and fat, respectively. How many daily grams of protein will the diet include?

123.75 g  

Step-by-step explanation:

You have three unknowns: protein (p), carbohydrate (c), and fat (f)

You need three equations for the three unknowns.  They are

(1)    p +   c +   f =    725

(2) 4p + 4c + 9f = 3500

(3) 4p         + 9f = 0.45(3500) = 1575

Subtract (3) from (2)

   4c = 1925

(4)  c =   481.25

Substitute (4) into (1)

    p + 481.25 + f = 725

(5) p +                f = 243.75

Multiply (5) by 4

(6) 4p + 4f = 975

Subtract (6) from (3)

  5f = 600

(7) f =   120

Substitute (7) into (3)

4p + 1080 = 1575

4p             =   495

 p             =    123.75

The diet will include 123.75 g of protein.

Check:

It checks.

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: