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# Ratio! Pls help kinda confuse -_-

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The number of chickens to the number of ducks on a farm was 6:5. After 63 ducks were sold, there were 3 times as many chickens as duks left.

a) How many chicken were there on the farm?

b) How many chickens and ducks were there altogetheron the farm in the end?

Guest Jan 6, 2015

#1
+92179
+5

The number of chickens to the number of ducks on a farm was 6:5. After 63 ducks were sold, there were 3 times as many chickens as ducks left.

I found this question a bit confusing too

We are told two things so we will need to set up 2 equations and solve them simultaneously.

$$\\\frac{6}{5}=\frac{C}{D}\qquad \rightarrow \quad C=\frac{6D}{5}\qquad \qquad \qquad (1)\\\\ \frac{3}{1}=\frac{C}{D-63}\quad \rightarrow \quad C=3(D-63)\qquad (2)\\\\$$

so

$$\begin{array}{rll} \frac{6D}{5}&=&3(D-63)}\\\\ \frac{2D}{5}&=&1(D-63)}\\\\ 2D&=&5(D-63)}\\\\ 2D&=&5D-315\\\\ 315&=&3D\\\\ D&=&105 \qquad \mbox{There were originally 105 ducks}\\\\\\ C&=&6*105\div 5\\\\ C&=&126 \qquad \mbox{There were originally 126 chickens}\\\\\\ \end{array}$$

$${\mathtt{105}}{\mathtt{\,\small\textbf+\,}}{\mathtt{126}}{\mathtt{\,-\,}}{\mathtt{63}} = {\mathtt{168}}$$

In the end there were 168 birds.

I did check that all these numbers make the original described situation true and you should do that too :)

Melody  Jan 6, 2015
Sort:

#1
+92179
+5

The number of chickens to the number of ducks on a farm was 6:5. After 63 ducks were sold, there were 3 times as many chickens as ducks left.

I found this question a bit confusing too

We are told two things so we will need to set up 2 equations and solve them simultaneously.

$$\\\frac{6}{5}=\frac{C}{D}\qquad \rightarrow \quad C=\frac{6D}{5}\qquad \qquad \qquad (1)\\\\ \frac{3}{1}=\frac{C}{D-63}\quad \rightarrow \quad C=3(D-63)\qquad (2)\\\\$$

so

$$\begin{array}{rll} \frac{6D}{5}&=&3(D-63)}\\\\ \frac{2D}{5}&=&1(D-63)}\\\\ 2D&=&5(D-63)}\\\\ 2D&=&5D-315\\\\ 315&=&3D\\\\ D&=&105 \qquad \mbox{There were originally 105 ducks}\\\\\\ C&=&6*105\div 5\\\\ C&=&126 \qquad \mbox{There were originally 126 chickens}\\\\\\ \end{array}$$

$${\mathtt{105}}{\mathtt{\,\small\textbf+\,}}{\mathtt{126}}{\mathtt{\,-\,}}{\mathtt{63}} = {\mathtt{168}}$$

In the end there were 168 birds.

I did check that all these numbers make the original described situation true and you should do that too :)

Melody  Jan 6, 2015

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