Welcome to our community

Be a part of something great, join today!

How many oranges were there in the morning?

  • Thread starter
  • Admin
  • #1

anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,632
There was a total of 748 oranges and apples at a fruit stall in the morning. By afternoon, the number of oranges sold was thrice the number of apples sold. The number of apples left was twice the number of oranges left. There were 22 more apples left than the apples sold.

How many oranges were there in the morning?

This primary math problem (as usual) can be solved without setting up equations and solve the simultaneous system of equations.

I welcome members to give it a try but nevertheless, I will post the solution tomorrow to showcase how Singapore model method works well in this kind of problem.
 
  • Thread starter
  • Admin
  • #2

anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,632
We can draw the following model based on the given information, and the top bar and lower bar are equal after we added another 5 units and 4 of 22 into them and this makes the sum of both bars becomes 748+5 units + 4(22).

\begin{tikzpicture}

\filldraw [fill=cyan, thick, draw=black] foreach \i in {-4,...,-3} { ({\i*1.8},0) rectangle ({(\i+2)*1.8},0.8) };
\filldraw [fill=cyan, thick, dotted, draw=black] foreach \i in {-1,...,2} { ({\i*1.8},0) rectangle ({(\i+2)*1.8},0.8) };
\filldraw [fill=magenta, thick, draw=black] (-7.2,-1) rectangle (-4.8,-0.2);
\draw[thick, dotted] (-4.8,0) -- (-4.8,-0.2);
\filldraw [fill=magenta, thick, draw=black] (-3.6,-1) rectangle (-1.2,-0.2);
\draw[thick, dotted] (-1.2,0) -- (-1.2,-0.2);
\filldraw [fill=magenta, thick, draw=black] (0,-1) rectangle (2.4,-0.2);
\draw[thick, dotted] (2.4,0) -- (2.4,-0.2);
\filldraw [fill=magenta, thick, draw=black] (3.6,-1) rectangle (6,-0.2);
\draw[thick, dotted] (6,0) -- (6,-0.2);
\draw[thick, dotted] (7.2,-1) -- (7.2,-0.2);
\draw[<->] (7.5,0.9) -- (7.5,-1);
\node at (9.4,-0) {748+5 units+4(22)};
\draw [<->] (6, -0.5) -- (7.2, -0.5);
\node at (6.6,-0.69) {22};
\draw [<->] (2.4, -0.5) -- (3.6, -0.5);
\node at (3,-0.69) {22};
\draw [<->] (-1.2, -0.5) -- (0, -0.5);
\node at (-0.6,-0.69) {22};
\draw [<->] (-4.8, -0.5) -- (-3.6, -0.5);
\node at (-4.2,-0.69) {22};
\node at (-6.3,0.5) {\small apple left};
\node at (-4.5,0.5) {\small apple left};
\node at (-2.7,0.5) {\small orange left};
\node at (-6,-0.6) {\small apple sold};
\node at (-2.4,-0.6) {\small orange sold};
\node at (1.2,-0.6) {\small orange sold};
\node at (4.8,-0.6) {\small orange sold};
\node at (-6.3,1.6) {\small 1 unit};
\draw [<->] (-7.2, 1.1) -- (-5.4, 1.1);
\node at (-6.1,-1.6) {\small 1 part};
\draw [<->] (-7.2,-1.4) -- (-4.8, -1.4);

\end{tikzpicture}

The problem is asking to find the sum of 1 unit and 3 parts, hence we have

$\begin{align*} 8\text{units}&=\dfrac{748+5\text{units}+4(22)}{2}\\&=\dfrac{836+5\text{units}}{2}\\16\text{unit}&=836+5\text{units}\\ 11\text{units}&=836\\1\text{unit}&=76\end{align*}$

$\begin{align*} 1\text{part}+22&=2(76)\\1\text{part}&=130\end{align*}$

Therefore there were $76+3(130)=466$ oranges in the morning.
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
426
I don't see any reason NOT to set up equations- they help to organize one' thoughts.
Let x be the number of oranges and let y be the number of apples in the fruit store in the morning. Let u be the number of oranges sold by afternoon and let v be the number of

There was a total of 748 oranges and apples at a fruit stall in the morning.
So x+ y= 748

By afternoon, the number of oranges sold was thrice the number of apples sold.
So u= 4v

The number of apples left was twice the number of oranges left.
The number of apples left was the number of apples in the morning minus the number of apples sold, y- v, and the number of oranges left is the number of oranges in the morning minus the number of oranges sold, x- u.

So y- v= 2(x- u) or 2x- y- 2u+ v= 0.

There were 22 more apples left than the apples sold.
So y- v= v+ 22 or y= 2v+ 22.

How many oranges were there in the morning?

This primary math problem (as usual) can be solved without setting up equations and solve the simultaneous system of equations.

I welcome members to give it a try but nevertheless, I will post the solution tomorrow to showcase how Singapore model method works well in this kind of problem.
We have four equations
x+ y= 748,
u= 4v,
2x- y- 2u+ v= 0, and
y= 2v+ 22

They can be solved for all of x, y, u, and v.
The problem is asking for the value of x.
 

Fantini

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
What is the Singapore model method?
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
426

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
  • Thread starter
  • Admin
  • #7

anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,632
What is the Singapore model method?
Hello Fantini! (Wave)

Singapore model method is a child-friendly pictorial language designed to develop students' understanding of fundamental mathematics concepts and proficiency in solving basic mathematics word problems. The model method affords higher ability children without access to letter-symbolic algebra as a means to represent and solve algebraic word problems. In Singapore, primary school children are taught a visual and concrete approach to solve arithmetic and/or algebraic word problems involving whole numbers, fractions, ratios and percents.

The model method focuses on the importance of representation. It builds upon children's knowledge of part-whole relationships in numbers. Children are taught to use appropriately sized rectangles to represent the information presented in word problems. In arithmetic problems, the rectangles represent specific numbers. By changing the role of the rectangles and using them to represent unknown quantities, the model method also can be used to depict algebraic word problems. Such representations effectively serve as pictorial equations.

The model method has proved to be an effective teaching tool for helping elementary aged children solve more word problems successfully.
 

Fantini

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
Do you have references where I could learn more about this method?
 
  • Thread starter
  • Admin
  • #9

anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,632
Of course!

You can explore these few links below to understand for more. Just so you know, if you find any problem that interests you and you want to figure out how to apply the model method on it, you can post it here and I will do my best (the hardest part for me comes of cranking out the code for TiKZ to display the model and that was why it took me more than a day to draw the model above) to guide you through it. :)

https://www.basic-math-explained.com/sg-math-drawing-models.html#.XxuOx-fLc2w

https://www.hmhco.com/~/media/sites.../math-in-focus/mif_model_drawing_lr.pdf?la=en