Question

A study showed that for young women a breakfast containing approximately 27 g (grams) of protein, 58 g of carbohydrate, 21 g of fat, and 525 calories is a nutritious breakfast that prevents a hungry feeling before lunch. The following table shows the content of four breakfast foods. How much of each should be served to obtain the desired amounts of protein, carbohydrates, fat, and calories? Calories Fat Carbohydrates Protein 110 0 24 2 1 cup juice 120 8 4. 8 1 cup cereal 100 6 10 2 slice bread 85 0 13 10 cup milk c juice c cereal slice(s) of bread c milk

Answer 1

1 C JUICE , 1 C MILK , 1.5 SLICE OF BREAD and 1.5 C CEREAL should each be served to obtain the desired amounts.

Explanation:

Given that;

protein carbohydrate fat calories

1 cup juice 2 24 0 110

1 cup cereal 8 4 8 120

1 slice bread 2 10 6 100

1 cup milk 10 13 0 85

Now let number of cups of juice, cereal , bread milk be

j, c, b and m respectively

from the table and information from the given

protein

2j + 8c + 2b + 10m = 27 ------------------equ 1

carbohydrate

24j + 4c + 10b + 13m = 58 ---------------equ 2

fat

8c + 6b = 21 ----------------------------------equ 3

calories

110j + 120c + 100b + 85m = 525 ------- equ 4

Now

equ 1 × 12 - equ 11

⇒(24j + 96c + 24b + 120m = 324) - (24j + 4c + 10b + 13m = 58)

= 92j + 14b + 107m = 266 -----------------equ 5

also

equ 1 × 55 - equ 4

( 110j + 440c + 110b + 550m = 1485) - ( 110j + 120c + 100b + 85m = 525 )

320c + 10b + 465m = 960

divide through by 5

64c + 2b + 93m = 192 ----------------------- equ 6

then

equ(5)×93 - equ(6)×107

(8556j + 1302b + 9951m = 24738) - (6848j + 214b + 9951m = 20544)

1708j + 1088b = 4194

divide through by 2

854j + 544b = 2097 --------------------------- equ 7

Now

equ(3)×854 - equ(7)×8

(6832c + 5124b = 17934) - ( 6832c + 4352b = 16776)

772b = 1158

b = 1158 / 772

b = 1.5

now put (b=1.5) in equation 3

8c + 6(1.5) = 21

8c 9 = 21

8c = 21 - 9

8c = 12

c = 12/8

c = 1.5

now put (b=1.5) and (c=1.5) in equation 6

64(1.5) + 2(1.5) + 93m = 192

96 + 3 + 93m = 192

93m = 192 - 99

93m = 93

m = 93/93

m = 1

now put (b=1.5), (c=1.5) and (m=1) in equation 1

2j + 8(1.5) + 2(1.5) + 10(1) = 27

2j + 12 + 3 + 10 = 27

2j + 25 = 27

2j = 27 -25

2j = 2

j = 2/2

j = 1

Therefore 1 C JUICE , 1 C MILK , 1.5 SLICE OF BREAD and 1.5 C CEREAL should each be served to obtain the desired amounts.