Question

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?​

Answer 1

123.75 g

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:

`\begin{array}{rcl}\\123.75 + 481.25 + 120 &=&725\\ 725 & = & 725\\&&\\4(123.75) + 4(481.25) + 9(120) &=& 3500\\495 + 1925 + 1080& =& 3500\\3500 &=& 3500\\&&\\4(123.75) + 9(120) &=& 1575\\495 + 1080&=& 1575\\1575&=& 1575\\\end{array}`

It checks.