How many chocolates did Angeline give to Billie

  • MHB
  • Thread starter anemone
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In summary: However, with "1 part + 1 unit= 70" you have y= 70. With "1 part+ 20= 1 unit", you have y= -20. Those are not the same so you have no solution.
  • #1
anemone
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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...(Nod))
 
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  • #2
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.
 
  • #3
[TIKZ]
\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};
[/TIKZ]

We are looking for the value of 1 unit.

$\begin{align*} 1 \text{ part}+1 \text{ unit}&=70\\1 \text{ part} +20&=1 \text{ unit}\\1 \text{ unit} -20&=70-1 \text{ unit}\\ 2 \text{ units}&=90\\ \therefore 1 \text{ unit}&=45\end{align*}$
 
  • #4
That would be better if you had said what "one unit" and "one part" are in terms of numbers of chocolates.
 

FAQ: How many chocolates did Angeline give to Billie

1. How many chocolates did Angeline give to Billie?

The number of chocolates that Angeline gave to Billie is not specified in the question. Therefore, we cannot provide an exact answer.

2. What is the significance of the number of chocolates given?

The significance of the number of chocolates given could vary depending on the context of the situation. It could represent a gesture of friendship, a reward for good behavior, or simply a gift. Without more information, we cannot determine the significance.

3. Why did Angeline give chocolates to Billie?

The reason for Angeline giving chocolates to Billie is not specified in the question. It could be for a special occasion, as a token of appreciation, or just a kind gesture. Without more information, we cannot determine the exact reason.

4. Did Billie like the chocolates?

The question does not mention whether Billie liked the chocolates or not. Therefore, we cannot provide an answer to this question.

5. How many chocolates did Billie receive from Angeline?

The number of chocolates that Billie received from Angeline is not specified in the question. It is also possible that Billie did not receive any chocolates at all. Without more information, we cannot determine the exact number.

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