Question

The following table gives the calories, fat, and carbohydrates per ounce for three brands of cereal. How many ounces of each brand should be combined to get 659 calories, 5.9 g of fat and 164.8 g of carbohydrates?

Cereal	Calories	Fat (g)	Carbohydrates (g)
All Fiber	50	0	22.0
Frosted Puffs	108	0.1	25.7
Natural Mixed Grain	127	5.5	18.0

All Fiber		oz
Frosted Puffs		oz
Natural Mixed Grain		oz

Answer 1

Solution:

Let ounces of fiber, frosted puffs, natural mixed grain be x, y, z  

50x + 108y + 127z = 659 .......(1)

0.1y + 5.5z = 5.9 ...........(2)

22x + 25.7y + 18z = 164.8 ...............(3)

From eq. (2),

y + 55z = 59 --> y = 59 - 55z

Put value of y in eq. (1) and (3)

50x + 108(59 - 55z) + 127z = 659 --> 50x - 5813z = -5713 .........(4)

22x + 25.7(59 - 55z) + 18z = 164.8 --> 22x - 1395.5z = -1351.5 ...........(5)

Multiply eq. (4) with 22 and eq. (5) with 50,

22(50x - 5813z = -5713) --> 1100x - 127886z = -125686 ...........(6)

50(22x - 1395.5z = -1351.5) --> 1100x - 69775z = -67575 ............(7)

Subtract (7) from (6)

-58111z = - 58111

z = 1

y = 59 - 55*1 = 4

x = 2

Therefore 2 ounces of all fiber, 4 ounces of Frosted puffs and 1 ounce of natural mixed grain should be combined to get 659 calories, 5.9g of fat and 164.8g of carbohydrates.

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