08 P5 Ratio Word Problem

Mrs Lee made some curry puffs and sardine puffs. The ratio of the number of curry puffs to the number of sardine puffs was 4 : 3. She made another 65 curry puffs and sold 27 sardine puffs. The ratio became 5 : 3. How many curry puffs did she make?

Strategy : Draw model systematically (e.g., translate each statement into the “model” form). Try to look at the models drawn and adjust accordingly. The challenge is to “simplify” or “reduce” the model into some common parts that we can find the value of the common part. There might be different parts in the model and the trick here is to express the different parts into 1 common part that we can find.

The ratio of the number of curry puffs to the number of sardine puffs was 4 : 3.

Possible questions to ask: Did she bake more curry puffs or sardine puffs? How many parts for curry puff ? How many parts for sardine puffs?

It should be quite easy to draw the model for most of the students.

She made another 65 curry puffs and sold 27 sardine puffs.

Possible questions to ask : What does “made another 65 curry puff more? Do I need to “add” or “take away” for the curry puffs ? What does sold 27 sardine puffs mean? Do I need to “add” or “take away” for the sardine puffs ?

The ratio became 5 : 3.

Possible questions to ask: Did she bake more curry puffs or sardine puffs? How many parts for curry puff ? How many parts for sardine puffs? Should I drawn another 2 bars to represent that ? Are the parts equal for both “before” and “after”?

Now, take a look at the model. What is wrong with the model ? For the curry puffs, does the models show “65 made” ? For the sardine puffs, does the models show “27 sold” ?

There is a need to adjust the model!

Now the model looks like this:

The trick is to find relationship between the red parts and the yellow parts.

For Curry Puffs

5 red parts = 4 yellow parts+ 65

1 red part = 4/5 yellow parts + 13

For Sardine Puffs

3 red parts = 3 yellow parts – 27

1 red part = 1 yellow part – 9

Now, we have 1 red part in common. Redraw the model to show the red part in terms of yellow part

From the diagram , is obvious that

1 part = 13+ 9

That is of course, not the final answer.Continue and try to find  what the question is asking for.