Here's how you can start.

Use guess-and-check by letting number of erasers be multiples of 3, e.g. 6 erasers ($2) and 22 pens ($44), etc. Then check if total is $36.

Primary schools penalise guess-and-check methods, unless you're P2 and below. Step 1: Assume all to be pen. Maximum possible cost is 28x2=$56 Step 2: Calculate how much your cost will be reduced if you have 1 less pen (aka you bought 1 set of 3 erasers). You would have to minus $6 (because you overestimated the cost by 3pens), and than add $1 (for the set of 3 erasers). So every time you reduce 1 pen from your assumption in Step 1, your cost reduces by $5. Step 3: Compare the actual cost. So Janice paid $36. The difference with the maximum possible cost is $20. So that means she has 4 sets of 3 erasers. Step 4: Double-check. 4 sets of 3 erasers = $4, 16pens = $32. Total $36. This is essentially a pattern question. Step 2 finds out the pattern that you would have otherwise seen in a guess-and-check table. But schools will look for a step-by-step solution.

There's no penalty to using guess and check or any plausible methods. As long as the method is sound, it'll receive equal respect.

Oh ok, thanks for clarifying :) though, it would be more educational to spot the patterns imo :) it would save time, especially in questions with bigger numbers.

It is a fact that there is no penalty with regards to marks awarded for the employment of the guess-and-check method during examinations. While I agree that all plausible methods should receive equal respect, not all methods are sound. Guess-and-check should always be the last resort to problem solving for such questions as I echo the sentiments of Marcus Ng that it can consume vast amount of time for the students. The penalty may not appear in the marks awarded, but it manifests itself in the lesser amount of time available to the students during examinations. My two cents.

When she wanted to double the number of bottles (8 to 16), she needed that 2 litres that was left over, plus 8 litres more. That means she needed 10 litres to make 8 bottles. Going back to the first 8 bottles, we know now that she used 10 litres and had 2 litres left over so she has 12 litres.

Sorry .. Did not understand 😔

After she made 8 bottles, she had 2 litres left. The 2 litres can be used for the next 8 bottles (so that she can have 16 bottles) but she's still short of 8 litres. That means she needs 10 litres for 8 bottles.

To fill 8 bottles, she needs 10 (2+8) litres of juice. So to fill 1 bottle, she needs 10÷8 = 1.25 litres She has 1.25 x 8 + 2 = 12 litres (Or she has 1.25 x 16 - 8 = 12 litres)

Thank u all.

Q15: In the kite, the 2 triangles are identical. Since base and height and 1 triangle is given, you can work out the area of each triangle and then the kite.

Q16: Volume of cylinder = base area*height. This means that height = volume/base area. Since the radius is given, we will be able to work out the height = 20pi/area of circle.