your Solve the following story problem using a system of linear equations. (a) Y

Question

your Solve the following story problem using a system of linear equations. (a) Your pet fish is malnourished. The veterinarian recommended that you feed your fish every day 48g of nutrient K, 56g of nutrient L, and 39g of nutrient M. Unfortunately, you've been unable to buy them separately. All you could find are these three fish foods: Xavier's (21g nutrient L plus 16g nutrient M per scoop), Yolando's (17g nutrient K plus 22g nutrient L per scoop) and Zander's (22g nutrient K plus 18g nutrient M per scoop). How many scoops of each fish food do you need to get the right amount of each nutrient?

Explanation / Answer

Solution:

It is recommended that you feed your fish every day 48g of nutrient K,

56g of nutrient L, and 39g of nutrient M

Now

Let you buy X scoops from Xavier's

therefore it contains

21X grams of nutrient L and 16X gram of nutrient M

again

Let you buy Y scoops from Yolando's

therefore it contains

17Y grams of nutrient K and 22Y gram of nutrient L

again

Let you buy Z scoops fromZander's

therefore it contains

22Z grams of nutrient K and 18M gram of nutrient M

form above

we can form follwoing equation

total gram weight of nutrient K to get the right amout

17Y + 22 Z = 48 ... (1)

total gram weight of nutrient L to get the right amout

21X + 22 Y = 56 ..(2)

total gram weight of nutrient M to get the right amout

16X + 18 Z = 39 .. (3)

from eqution (1) and (2) and (3)

on solving them we get

X = 4251/3619 Scoop

Y = 451/329 Scoop

Z= 8125/7238 Scoop

thus

you need to buy X= 4251/3619 Scoops and Y = 451/329 Scoops and Z= 8125/7238 Scoops of each fish food you need to get the right amount of each nutrient

Answer

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