Question 1:
Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim's sweets to chocolates became 1 : 7 and the ratio of Ken's sweets to chocolates became 1:4. How many sweets did Ken buy?.
Answer:
Rule 1: write down rule:
Js: Jc
-12
1 : 7
Ks: Kc
-18
1 4
Must understand that here is 2 sets of ratio, so if you says jim is units, ken has to be parts:
ie:
Js: Jc
-12
1u : 7u
Ks: Kc
-18
1p 4p
Catch hint: Jc didnt change, Ks didnt change.
This shows that at first after they give each other cho and sweets, Jim got 7units of chocolates, Ken got 1p of sweets.
and remember that both have same number of sweets:
1p - 12 = 1u
and remember that both have same number of chocolate:
7u - 18 = 4p
rewrite 1p - 12 = 1u
: 1u + 12 = 1p
7u - 18 = 4p
students should know how to do those 4 mangoes and 3 oranges cost how much questions.
Normally they will write down 2 rows of info and start to do comparing.
If find oranges, make the mangoes the same!
Since i know sweets for ken no change is 1 part, i want to find part, so make the unit the same:
1u + 12 = 1p
7u - 18 = 4p
becomes: 1u = 1p - 12
<---- all x7x7x7 7u = 4p + 18
7u = 7p - 84
by now should know a lot of maths working do comparing, compare aka MINUS. so 7p - 4p = 3parts
+18 and -84 are opposite symbols.
this is inline with the happy n sad faces method for those teachers give students how many chocolates and leftover or short of how many cho questions:
3parts -> 84+18 = 102
1 part -> 34
remember this is the answer after the ken n jim give half of what they have to each other.
so ken bought 2x34 = 68.
Question 2:
Mei and Lin were in a bicycle race. Mei was travelling at a constant speed of 20km/hr and they both did not change their speed. When Lin completed half the race, Mei was 3.5km ahead. Mei completed the race at 10.45am. What time did Lin complete the race?
Logic is:
Lin travel half, Mei travel half too plus another 3.5km.
Lin travel another ha;f, Mei travel another half and another 3.5km.
so analysis is:
Lin travel whole thing when Mei travel finish plus extra 7km.
But in the story, Mei finish on the dot only no extra, so you rewind the whole "Tape":
Mei rewind by 7km:
T = D/S
= 7/20 hr
= 21mins
by means Lin also rewind by 21mins. this shows that if u restart the tape, Lin needs another 21mins to reach the place. so he will take 10.45am + 0021 = 11.06am.
Question 3:
Sally baked some cookies to sell. 3/4 of them were chocolate cookies and the remaining were almond cookies. After she sold 5/6 of chocolate cookies and 210 almond cookies, she had 1/5 of the cookies left. How many cookies did she sell?
Cho -> 3/4
Alm -> 1/4
cho left -> 1/6 x 3/4
-> 1/8
assume that alm didnt sell off, so alm + cho left should be:
1/8 + 1/4 = 3/8
so almond sold should be:
3/8 - 1/5 = 15/40 - 8/40
= 7/40
7/40 -> 210
1/40 -> 30
cho sold -> 5/6 x 3/4 = 5/8 = 25/40 which is 25x30 = 750
total sold = 750 + 210 = 960
Question 4:
Curry puff shop sells puffs at $0.80 each. Offer:Buy 3 get 4th half price. If customer has $50, how many puffs can he buy if he buys as many as he can.
This is packet rule question:
1 packet inside pack 2 puffs since pple will want to grab the offer:
3x0.80 = 2.40
one half price = 0.40
so get 1 packet aka 4 puffs = 2.40+0.40 = 2.80
$50 / 2.80 = 17 packets and left $2.40 change.
2.40 can get 3 loose puffs, which is a sad case coz the person is entitled to buy the 4th at cheaper price but not enough money already :S
so 17 packets = 17x4 = 68 puffs
68 + 3 loose = 71
Question 5:
String of 2 big balloons is 90cm String of 5 small balloons is is 1.2m If both strings are of the same length, there would be 105 more small balloons than the big balloons. How many balloons are there altogether?
If both strings are of the same length
This is a hint for LCM question, ie write time table!!
90cm, 180,270,360.
1.2m, 2.4,3.6.
See above: both string is of same length : but
Big ballons = 4x2=8
small balloons = 3x5=15
For 3.6m of string, small balloons is more than big balloons is: 15-8 = 7
105 more compare to this 7 means it is 15 times more.
small n big balloons for one time is 8+15 = 23
ans = 23 x 15 = 345
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