Algebra, STD2 EQ-Bank 30

Eleni is a farmer who sold chickens and ducks at the local market.

Each chicken was sold for $15 and each duck was sold for $9.

She sold a total of 78 birds for a total of $930.

By writing two equations to represent this information, find the number of chickens and the number of ducks Eleni sold. (3 marks)

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$\text{Chickens}=38, \ \text{Ducks}=40$

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$\text{Let}\ x=\text{chickens},\ y=\text{ducks}$

$15x+9y=930\ …\ (1)$

$x+y=78\ \ \Rightarrow \ y=78-x\ …\ (2)$

$\text{Substitute}\ \ y=78-x\ \ \text{into (1):}$

$\text{Substitute}\ \ x=38\ \ \text{into (2):}$

$y=78-38=40$

$\therefore\ \text{Eleni sold 38 chickens and 40 ducks.}$