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Question

Pls help me solve this qn using simultaneous equations. Thx!

Answer

Let the number of ducks be x and the number of goats be y.

There are 30 animals together because there are 30 heads and each animal only has one head. Therefore, the relationship between the number of ducks and the number of goats is:

x + y = 30 — Equation 1

Now we need a second equation because this is simultaneous equations. There are 2 things that is not in the questions but you should know for sure:

  1. Ducks have 2 legs
  2. Goats have 4 legs

The total number of legs ducks have is 2 * x, the total number of legs goats have is 4 * y.

2x + 4y = 94 — Equation 2

From Equation 1:

x + y = 30

y = 30 – x

Substitute this into Equation 2:

2x + 4 (30-x) = 94

Expand the brackets:

2x + 120 – 4x = 94

120 – 2x = 94

2x = 26

x = 13

y = 30 – x = 30 – 13 = 17

There are 13 ducks and 17 goats.

Hope this helps!

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