Solve the following questions. Solve the following story problem using a system

Question

Solve the following questions.

Solve the following story problem using a system of linear equations. 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

Sorry about first problem

Solution part (a):

Let x= number of chicken

y = number of goats,

Given that there are total 20 animals, it means

x + y = 20 -------(i)

And since the number of chicken legs is 2 times the number of chickens (2x),and the number of goats legs is 4 times the number of goats(i.e., 4y)   then the total number of legs is 2x +4y.
But you are told that this number is 56. So we can write the equation:

2x+4y =56 ------(i)

solving equation (i) and (ii)

from (i) , x+y =20 => y = 20 - x , substitute in (ii)

2x + 4(20 - x) = 56 => 2x + 80 - 4x = 56

-2x = - 24

x= 12, substitute in (i)

12 +y = 20

y=8

checking: 12 * 2( chikens legs ) + 8 *4 (goats legs) = 24 + 32 =56 (verified)

Therefore, Number of chickens are 12, goats are 8

(b)

let say a = number of hot dogs

b =nunber of sodas

The person in front of you ordered 3 hot dogs (3a ) and 2 sodas (2b), total cost for this is $ 12.50,

We write in terms of linear equation

3a + 2b = 12.50 -------(1)

Similarly, Another person oders are 4 hot dogs(4a) and 3 sodas (3b) , total cost $ 18.25

We write in terms of linear equation

4a + 3b =18.25 -----(2)

Solving (1) and (2)

We got, a =$ 1, b = $ 4.75

but we need to find

How much will your order of 2 hot dogs and 1 soda

ie,

= 2 a + 1 b

= 2 *1 + 1 * 4.75

= 2 + 4.75

=$ 6.75

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.