Vanilla Cake:

firebird:

Dear maths guru

Please help me on the following maths:

Hi Firebird,
Pls refer to the below workings done by Vanilla Cake, this morning. Due to time constraint, she didn't complete the speed question(she was in a rush to go to school). Sorry, pls wait for others like Dharma etc to help.If you don't mind, could you pls advise the source of these questions? The ones on ratio and speed are interesting and I will let DD2 to practise.
Thks.

VC's mum

firebird:

1) John had $180 more than Raymond at first. Both bought a different printer with some of their money. In the end Rayamond was left with $20 more than John. If John's printer cost 50% more than Raymond's printer, how much does John's printer cost?

John's printer-> 150%
Raymond's printer -> 100%
$(180+20)= $200
50% -> $200
150% -> $600

Cost of John's printer = $600

firebird:

2) At 9am John was cycling from Point A to Point B. At the same time, Mary was cycling from point B to point A using the same route as John. Cycliing at a speed of 4km/h faster than Mary, they would pass each other 300 meter away from the mid point.
a) What time did they pass each other?
b) If John took another 3 minutes to reach Point B, what time would Mary reach Poin A?

0.3/4 = 0.075 h = 4.5 min
Add 4.5 min to 9 am -> 9:04:30
(a) They passed each other at 9:04:30

(b) Not enough time to think and solve, pls wait for others to solve.

firebird:

3) Daniel had 40% more stickers than Brandon. Daniel and Brandon each gave 20% of their stickers to Calvin. As a result, Calvin's stickers increased by 80%. If Daniel has 20 more stickers than Calvin in the end, how many stickers did Brandon have at first?

Before
140%
B: 100%
u

After
112%
B: 80%
u+28%+20% = u+48%

80% increased for C-> 180/100xu = 1.8u

1.8u=u+48%
0.8u=48%
u=60%

60%+48% = 108%
Difference between D and C -> D-C=112%-108% = 4%
4% -> 20
100% -> 20/4x100=500

At first, Brandon had 500 stickers.

firebird:

4) At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.
a) Find the ratio of male speakers to male participants at the conference.
b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants remaining behind. How many speakers were there at the conference?

This is a trick question and you have to know the common difference is 3u as the number of male and female participants was the same.

Total
M : W
120 : 100
6 : 5
18: 15

Speakers
M : W
8 : 5
Total speakers = 13u (8u+5u)

Participants
M : W
10 : 10

8: 10
(a) Ratio of male speakers to male participants = 8 : 10 = 4 : 5

I use cross multiplication to solve this, you may wish to use alternative methods to suit you.

(10u-40)/(10u+60)=3/4
30u+180=40u-160
10u=340
u=34
13u=442

Number of speakers at the conference = 442

Check
Speakers
M: 272
W: 170

Participants
M: 340
F: 340

Total
M: 612
W: 510

Phew, done except for speed part (b).Pls check all my calculations, thanks.

Hi there, for the above question on Speed, we need to take into consideration the time traveled by Mary as well. There is a difference of 300m which takes 4.5 mins to travel. Assuming they start at 9am at the same time, John traveled 4km/h faster than Mary which gives him a head start of 300m. Thus, Mary and John would have traveled for 9mins while John traveled 300m more. The answer should be 9:09am instead.

How do you solve part b?