Question

A glass of skim milk supplies 0.1 mg of iron, 8.5 g of protein, and 1 g of carbohydrates. A quarter pound of lean red meat provides 3.4 mg of iron, 22 g of protein, and 20 g of carbohydrates. Two slices of whole-grain bread supply 2.2 mg of iron, 10 g of protein, and 12 g of carbohydrates. If a person on a special diet must have 35 mg of iron, 224 g of protein, and 200 g of carbohydrates, how many glasses of skim milk, how many quarter-pound servings of meat, and how many two-slice servings of whole-grain bread will supply this?

Answer 1

Answer:

glasses of milk=4

quatar pounds servings of meat =5

two slices of whole grains bread =8

Step-by-step explanation:

Let m= milk

r=meat

b=bread

0.1m+3.4r+2.2b=35 (1)

8.5m+22r+10b=224 (2)

m+20r+12b=200 (3)

Multiply (1) by 85 and (2) by 1

8.5m+289r+187b=2,975 (4)

8.5m+22r+10b=224 (5)

Subtract (5) from (4)

267r+177b=2,751 (6)

Recall,

8.5m+22r+10b=224 (2)

m+20r+12b=200 (3)

Multiply (2) by 1 and (3) by 8.5

8.5m+22r+10b=224 (7)

8.5m+170r+102b=1700 (8)

Subtract (7) from (8)

148r+92b=1,476 (9)

Recall,

267r+177b=2,751 (6) and

148r+92b=1,476 (9)

Multiply (6) by 148 and (9) by 267

26196b=407,148 (10)

24564b=394,092 (11)

Subtract (11) from (10)

1,632b=13,056

Divide both sides by 1,632

b=13,056/1,632

b=8

Substitute the value of b in (9)

148r+92b=1,476 (9)

148r+92(8)=1,476

148r+736=1,476

148r=1,476-736

148r=740

Divide both sides by 148

r=740/148

r= 5

Substitute the value of b and r in (1)

0.1m+3.4r+2.2b=35 (1)

0.1m+3.4(5)+2.2(8)=35

0.1m+17+17.6=35

0.1m+34.6=35

0.1m=35-34.6

0.1m=0.4

Divide both sides by 0.1

m=0.4/0.1

m=4

4 glasses of milk, 5 quatar pounds servings of meat and 8 two slices of whole grains bread will supply the required nutrients.