# How many chocolates did Angeline give to Billie

#### anemone

##### MHB POTW Director
Staff member
Angeline and Billie shared some chocolates. Angeline had 70 more chocolates than Billie. After Angeline gave 20% of her sweets to Billie, Billie had 20 more chocolates than Angeline. How many chocolates did Angeline give to Billie?

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

#### Country Boy

##### Well-known member
MHB Math Helper
That looks like a pretty standard "algebra" problem. Let x be the number of chocolates Angeline had and let y be the number of chocolates Billy had.

" 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.

#### anemone

##### MHB POTW Director
Staff member
\begin{tikzpicture}

\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*}

#### Country Boy

##### Well-known member
MHB Math Helper
That would be better if you had said what "one unit" and "one part" are in terms of numbers of chocolates.