1. Mr Lim spent $1496 on some comics and dictionaries altogether. The number of comics bought to the number of dictionaries bought was in the ratio 3:2. A dictionary cost $4 more than a comic. The total cost of the comics was 20% more than the total cost of the dictionaries. Find the cost of the a dictionary.
2. Marvin bought a box of fruits. 30% of the fruits are apples and the rest oranges. He realised that half of the apples were rotten and threw them away. He then bought some oranges and the number of oranges increased by 40%. After that, he found out that there were 52 more fruits in the box. How many fruits were there in the box at first?
3. Ann and Ben were given some money each. If Ann spent $25 each week and Ben spent $75 each week, Ann would still have $1350 left when Ben had sepnt all his money. If Ann spent $75 each week and Ben spent $25 each week, Ann would still have $150 left when Ben had sepnt all his money.
(a) How much money did Ann receive?
(b) How much money did Ben receive?
Hi,
Could you please highlight what difficulties you are facing, when solving these questions?
Ultimately, it is the student who sits for the exam.
Thanks!
Cheers,
Wen Shih
I'm posting this on behalf of my daughter who is sitting for PSLE this year. She was not sure how to do these problems. Thanks.
For qn 1.
Cost of Dictionary is $20. I'm not explaining the answer because I used algebra and a calculator. Haha...since when did PSLE become so hard?
Ask your daughter to wait for her teacher to explain.
Or anyone can do the sum in a simpler manner?
2. Marvin bought a box of fruits. 30% of the fruits are apples and the rest oranges. He realised that half of the apples were rotten and threw them away. He then bought some oranges and the number of oranges increased by 40%. After that, he found out that there were 52 more fruits in the box. How many fruits were there in the box at first?
30% apples 70% oranges
15% apples 98% oranges (70% + (70%x40%)) (13% over 100%)
Therefore, 13% = 52
1% = 4
100% = 400
This seems to be the answer.
Originally posted by kkhing:Ann would still have $1350 left when Ben had sepnt all his money.
After how many weeks?
Or do we have to find it out ourselves?
Qns 1 Solution
First, find the total cost of the comics ($816) and dictionaries ($680).
Then find the cost of 1 unit of comics ($272) and dictionaries ($340).
1 unit of D - 1 unit of C = $68
Quantity in 1 unit = $68/$4 = 17
Therefore, there are 51 comics and 34 dictionaries.
C = D - $4
51C = 51D - $204
51D - $204 + 34D = $1496
85D = $1496 +$204 = $1700
D = 1700/85 = $20
~Solved by a friend
Qns 3 Solution
A I
B III
A III III III
B I I I
I -> a unit of $25
the 1st model is a set of 1 week while the 2nd model is a set of 3wks. since we know that Ben spent 1/3 as much in the second scenario, the no. of wks in the second scenario is thus 3 times as long.
if we group a set of 3 wks together (as in the 2nd model drawn), there'll be the same no. of sets for both models drawn.
In a single set (1wk for 1st model, 3 wks for 2nd model), there's a difference in the how much Ann spent, which is 8 units of $25 = $200.
In the total number of sets, the difference in how much Ann spent is $1350 - $150 = $1200.
Hence, to find the number of sets, $1200/$200 = 6 sets
This implies that the first scenario takes 6 wks while the second scenario takes 6x3=18wks. from here it's easy to get to the answer using either the first or second scenario.
a) $1500 b) $450