Hi, can anybody help solve these questions without the use of algebra? My sis is in P6 and she doesn't have the knowledge of solving algebraic / simultaneous equations... Many thanks!
1) John had 239 male and female fishes. 3/5 of the male fishes died and he bought another 14 more female fishes. As a result, the number of female fishes he had was 1/4 of the number of male fishes. How many male and female fishes were there at first?
2) A jar contained some red and blue erasers. At first, the number of red erasers was 75% of the blue erasers. After adding in another 3 erasers of each colour, the number of red erasers becomes 80% of the number of blue erasers. How many erasers of each colour were there at first?
3) In a classroom, when a boy stands up, the number of boys sitting becomes 4/5 of the number of girls sitting. On the other hand, when a girl stands up, the number of girls sitting becomes 8/7 of the number of boys sitting. How many boys and girls are there in the class?
4) The ratio of $2 notes to $5 notes in James' piggy bank was 13:8 He exchanged 20 pieces of $2 notes for some $5 notes, after which, the ratio of $2 notes to $5 notes became 4:5. What was the total value of $2 notes and $5 notes in the piggy bank at first?
Answers to any questions will be very much greatly appreciated! =)
Thank you very much in advance!
Q1.
After:
M: U U U U (4units)
F: U (1unit)
Before:
M: U U U U U U U U U U(10units, since 4units are left after 3/5 died)
F: U - 14female fishes
Therefore, at first there are all together 11units - 14fishes. which is 239.
11units should represent 239+14=253 fishes
1unit represents 253/11=23 fishes.
No. of Male fishes = 10units =230
No. of Female fishes = 1units - 14 = 23 - 14 = 9 (or 239 - 230 = 9)
Q2.
75% is 3/4. At first,
R: U U U (3units)
B: U U U U (4units)
So 3units + 3 is 80% of 4units +3
(3units + 3 ) x 5 is 80% x 5 of 4units + 3
15units + 15 is 4 times of 4units + 3
while 4 times of (4units +3) is 16units + 12
Since 15units + 15 and 16units + 12 are equal, 1unit = 3
R: 3 x 3 = 9. B = 4 x 3 =12
Q3.
When a boy stands up, no. boys sitting : no. of boys sitting = 4 : 5
So in this classroom, ORIGINALLY,
no. of boys = 4units+1
no. of girls = 5units
Now when a girl stands up, the no. of girls sitting becomes 5units - 1, and this is 8/7 of 4units +1
8/7 of (4units + 1) is 32/7 units + 8/7 which is equal to 5units -1
So 8/7 + 1 and 5units - 32/7 units are the same
15/7 and 3/7 units are the same
15 and 3units are the same
1unit = 5.
no. of boys = 4 x 5 + 1 = 21; no. of girls = 5 x 5 = 25
Q4.
Originally,
no. of $2 notes = 13units
no. of $5 notes = 8units
After 20 pieces of $2 notes are exchanged to 8 pieces of $5 notes
no. of $2 notes becomes 13units - 20
no. of $5 notes become 8units + 8
Now (13units - 20) is 4/5 of (8units + 8)
4/5 of (8units + 8) is 32/5 units + 32/5, which is equal to 13units - 20
Therefore 32/5 + 20 and 13units - 32/5units are equal
132/5 and 33/5 units are equal
132 and 33units are equal
1unit = 132/33 = 4
Total value = 13units of $2 + 8units of $5 = 13 x 4 x $2 + 8 x 4 x $5 = $104 + $160= $264.
PS: Your sister is very weak at the problem sum of this topic - ratio, all these 4 questions are of the same type in fact. Therefore, I suggest your sister go and find a tutor (at least a temp one) and help her to excel in this topic first.
Hi frekiwang, thanks a lot for the solutions! I didn't realise that all 4 questions could be solved without using simultaneous equations. Thanks! =)
You are welcome, but make sure your sisiter know how to solve this type of questions in future as most likely one question in PSLE is of this type.
look wat our poor 12-year-olds are going thru.....................