Question

Mrs. Monty bought ten chickens and four ducks for $274. However, if she had purchased four chickens and three ducks, the total cost would have been S160. i. Write down a pair of simultancous cquations to represent the information given above. Use c to represent the cost of a chicken, and d to represent the cost of a duck. (2 marks) ii. Calculate the cost of one chicken, as well as the cost of one duck: ( 8 marks)

Answer 1

i.

System of equations:

10c + 4d = 274

4c + 3d = 160

ii.

Costs:

Chicken: $13

Duck: $36

Explanation:

i.

The system of equations is:

10c + 4d = 274

4c + 3d = 160

ii.

Solution:

Multiply the first equation by -3. Multiply the second equation by 4. Add the equations.

-30c - 12d = -822

(+) 16c + 12d = 640

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-14c = -182

c = -182/-14

c = 13

Substitute 13 for c in the second original equation and solve for d.

4c + 3d = 160

4(13) + 3d = 160

52 + 3d = 160

3d = 36

Answer:

System of equations:

10c + 4d = 274

4c + 3d = 160

Costs:

Chicken: $13

Duck: $36