Answer:
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:
[tex]\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}[/tex]
It checks.
