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

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.

Step-by-step 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.

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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