- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,642

(This is another word problem that can be approached by the model method...)

- Thread starter anemone
- Start date

- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,642

(This is another word problem that can be approached by the model method...)

- Jan 30, 2018

- 428

" Angeline had 70 more chocolates than Billie."

x= y+ 70 or y=x- 70.

" After Angeline gave 20% of her sweets to Billie, Billie had 20 more chocolates than Angeline."

20% of Angeline's sweets is 0.2x. After Angeline gives them to Billie she has x- 0.2x= 0.8x and Billie has y+ 0.2x sweets. y+ 0.2x= 0.8x+ 20. Subtract 0.2x from both sides to get y= 0.6x+ 20.

We have both y= x- 70 and y= 0.6x+ 20 so x- 70= 0.6x+ 20.

Solve that for x.

" How many chocolates did Angeline give to Billie?"

Multiply x by 0.2.

- Thread starter
- Admin
- #3

- Feb 14, 2012

- 3,642

\draw (0,0) rectangle (2,1);

\draw (-8,0) rectangle (0,1);

\draw [<->] (-8, 1.4) -- (0.8, 1.4);

\node at (-3,1.6) {\small 4 units};

\draw [<->] (0, 1.2) -- (2, 1.2);

\node at (1,1.8) {\small 70 chocolates};

\node at (0.4,0.4) {\tiny 1 part};

\node at (1.4,0.4) {\tiny 1 unit};

\draw[thick, dotted] (0.8, 0) -- (0.8, 1);

\node at (-8.6,0.5) {\small A};

\node at (-8.6,-1) {\small B};

\draw (-8,-1.5) rectangle (0,-0.5);

\draw (0,-1.5) rectangle (1.2,-0.5);

\draw[thick, dotted] (0.8, -1.5) -- (0.8, -0.5);

\node at (0.4,-1) {\tiny 1 part};

\node at (1,-1) {\tiny 20};

\draw[very thick, dotted,green] (0,-1.5) rectangle (1.2,-0.5);

\draw[ultra thick, dotted,green] (0,-1.5) rectangle (1.2,-0.5);

\draw[ultra thick, dotted,green] (0.8,0) rectangle (2,1);

\draw[gray, thick, - >] (2.1,0.5) -- (2.2,0.5) -- (2.2,-1) -- (1.3,-1);

\draw [<->] (0,-1.7) rectangle (1.2,-1.7);

\node at (0.7,-1.85) {\tiny 1 unit};

\end{tikzpicture}

We are looking for the value of 1 unit.

$\begin{align*} 1 \text{ part}+1 \text{ unit}&=70\\1 \text{ part} +20&=1 \text{ unit}\\1 \text{ unit} -20&=70-1 \text{ unit}\\ 2 \text{ units}&=90\\ \therefore 1 \text{ unit}&=45\end{align*}$

- Jan 30, 2018

- 428