 ## Question

secondary 3 | A Maths

Anyone can contribute an answer, even non-tutors.

##### Mary

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Date Posted: 10 months ago
Views: 191
Eric Nicholas K
10 months ago
Q18

Q19

In a span of 12 days, Rick had gone from "learning five times as long as Nic" to "learning twice as long as Nic".

We assume that they study at the same rate.

Let Nic's initial number of days studied be t days (during two weeks ago).

Rick's initial number of days studied is 5t days.

Twelve days later (i.e. two days ago),

Nic: (t + 12) days
Rick: (5t + 12) days

As it turned out, Rick ended up learning only twice as much as Nic, so

5t + 12 = 2 (t + 12)
5t + 12 = 2t + 24
3t = 12
t = 4

So two weeks ago, Nic studied for 4 days and Rick studied for 20 days.

Today,
Nic: 18 days
Rick: 34 days
Total: 52 days

This question can be done using ratio approaches also, by converting the ratios 5 : 1 and 2 : 1 into 5 : 1 and 8 : 4 respectively to reflect the case where the difference (of 3 units studied) remains unchanged.
Mary
10 months ago
Hi, for qn18 the shaded area is where the isosceles triangles overlap one another. Thank you
Eric Nicholas K
10 months ago
Q20

I believe that when 4 : 3 is being scaled, it will get "stuck" at 12 : 9 (because the limit for the 16 : 9 screen is 9 units tall)

So, 4/16 of the screen, or 1/4 of the screen, is black.

Similarly, when 16 : 9 is being scaled, it will get stuck at 4 : 2.25 (because the limit for the 4 : 3 screen is 4 units wide)

So, 0.75/3 of the screen, or 1/4 of the screen, is black.

The required ratio is 1/4 : 1/4, or 1 : 1.
Mary
10 months ago
Thank you very much, Happy Chinese New Year! 