Q&A - PSLE Math

[MathIzzzFun]

happyheart:

Hi,

Need help to solve these using model please.

Q) If Jeremy gives 15 stickers to Ramesh, he will have four times as many stickers as Ramesh. If Ramesh gives 5 stickers to Jeremy, the ratio of Jeremy's stickers to Ramesh stickers would be 14:1. How many stickers does Jeremy have?

Thank you!

other than model method, you can use cross-multiply/unit & parts method,
here's a solution using cross-multiply method.. here are some other solutions using the cross-multiply method in this forum:

http://tinyurl.com/ksp-Xmultiply

...If Jeremy gives 15 stickers to Ramesh,
Jeremy's stickers : Ramesh's stickers --> 4u : 1u

At first, Jeremy's stickers : Ramesh stickers --> 4u + 15 : 1u - 15 ** add the 15 stickers to Jeremy's and remove 15 from Ramesh's

If Ramesh gives 5 stickers to Jeremy,
Jeremy's stickers : Ramesh's stickers --> 4u+15 +5 : 1u-15 -5
--> 4u + 20 : 1u - 20
= 14 : 1

cross-multiply
4u + 20 = 14u - 280
10u --> 300
1u --> 30

Jeremy's stickers --> 4 x 30 + 15 = 135

if you need the solution model, I will try to post it when I find some time.

cheers.

[mathnoobs]

StaryNight:

lee tong fong:

Can you please help to solve another 2 more problem sum, thanks in advance


1)In July, Pauline spent 20% of a sum of money on tuition, 60% on food and saved the rest. In August, the sum of money was increased by 15%. She spent the same amount of money on tuition but increased her saving by 30%. She saved $390 in August.
a)How much money did she spend on tuition in July?
b)How much did she spend on food in August?

2) Azman had 25% more marbles than chongfu. Chongfu has 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio 3:1 . In the end, Azman and Bala had 780 and 480 marble left respectively. How many marbles did Azamn have at first?

Hi lee tong fong,
this is the solution for the first question:
130/100 x 20 = 26 (% of money saved in August)
26%--> $390
1%--> $390/26 = $15
20%--> $15x20=300 (ans for part a)

(b)
100%--> 15x100=1500 (total sum of money in july)
1500-300-390=810 (ans for part b)

Hope this helps!

I'm afraid I'm a bit confused here.
for part (b), should not the 100% = total sum of money in Aug ? which is 115% of 1500 ? since there was an increase of 15% in the sum of money ?
if worked out in this way, the answer for part (b) is not 810.

[lee tong fong]

Thanks for your help to solve my earlier questions. I have further questions to seek your help.


1)\tJoseph has some local and foreign stamps in 2 boxes. In Box A, the numbers of local and foreign stamps are in the ratio 3: 4. In Box B, the number of local stamps is twice the number of foreign stamps. Joseph transfers half of the foreign stamps from Box A to Box B. The numbers of stamps in Box A become 105 and the ratio of the number of local stamps to the number of foreign stamps in Box B becomes 6:5.
a)\tHow many foreign stamps have been transferred from Box A to Box B?
b)\tWhat is the number of stamps in Box B at first?

2)\tRavi had a total of 80 pieces of $10 notes and $50 notes. He used ½ of his $10 notes and withdrew another four pieces of $50 notes from the bank. After which, the number of $50 notes he had was 2/5 the number of $10 notes. Find the total value of the 80 pieces of notes he had at first.

3) 2/9 of Rani’s balloons were red and the rest were green. She gave away 15 green balloons and bought another 25 red balloons. She then had the same number of red and green balloons. How may green balloons did she have at first?

Thanks in advance.

[happyheart]

MathIzzzFun:

happyheart:

Hi,

Need help to solve these using model please.

Q) If Jeremy gives 15 stickers to Ramesh, he will have four times as many stickers as Ramesh. If Ramesh gives 5 stickers to Jeremy, the ratio of Jeremy's stickers to Ramesh stickers would be 14:1. How many stickers does Jeremy have?

Thank you!

other than model method, you can use cross-multiply/unit & parts method,
here's a solution using cross-multiply method.. here are some other solutions using the cross-multiply method in this forum:

http://tinyurl.com/ksp-Xmultiply

...If Jeremy gives 15 stickers to Ramesh,
Jeremy's stickers : Ramesh's stickers --> 4u : 1u

At first, Jeremy's stickers : Ramesh stickers --> 4u + 15 : 1u - 15 ** add the 15 stickers to Jeremy's and remove 15 from Ramesh's

If Ramesh gives 5 stickers to Jeremy,
Jeremy's stickers : Ramesh's stickers --> 4u+15 +5 : 1u-15 -5
--> 4u + 20 : 1u - 20
= 14 : 1

cross-multiply
4u + 20 = 14u - 280
10u --> 300
1u --> 30

Jeremy's stickers --> 4 x 30 + 15 = 135

if you need the solution model, I will try to post it when I find some time.

cheers.

I can understand the soulution but confused as to why you cross multiply? How to I explain to DS? Thanks.

[Skyed]

lee tong fong:

Thanks for your help to solve my earlier questions. I have further questions to seek your help.


2)\tRavi had a total of 80 pieces of $10 notes and $50 notes. He used ½ of his $10 notes and withdrew another four pieces of $50 notes from the bank. After which, the number of $50 notes he had was 2/5 the number of $10 notes. Find the total value of the 80 pieces of notes he had at first.

Let the number of $10 notes be x.
Let the number of $50 notes be y.

x + y = 80 ---(1)

y+4/0.5x = 2/5 -----(2)

crossmultiply in (2), x = 5y + 20 ---(3)

sub (3) in (1), 5y + 20 + y = 80
6y = 60
y = 10
therefore x = 70

total value = 70(10) + 10(50) = answer

[Skyed]

lee tong fong:

3) 2/9 of Rani’s balloons were red and the rest were green. She gave away 15 green balloons and bought another 25 red balloons. She then had the same number of red and green balloons. How may green balloons did she have at first?

Thanks in advance.

Let the number of red balloons be x.
Let the number of green balloons by y.

x/y = 2/7
therefore crossmultiply, 7x = 2y -----(1)

y - 15 = x + 25
y = x + 40 --- (2)

From (1), y = 3.5x ---(3)

sub (3) in (2), 3.5x = x + 40
therefore x = 16

therefore y = 16 + 40 = 56

[lee tong fong]

Thanks for the solution. How do you form the equation for cross-multiply and why you need to cross-multiply.


Can you provide alternative solution using model?

[Skyed]

lee tong fong:

Thanks for the solution. How do you form the equation for cross-multiply and why you need to cross-multiply.


Can you provide alternative solution using model?

Hi for the equation for cross multiply, say, since you know the ratio of green is to blue is 2:3, so if you write is as a fraction, it will be like g/b = 2/3

Cross multiply is to get a single equation so that you can use substition later.

And sorry I'm in Sec 4 and can't really remember the \"model\" method used in primary school :3

[lee tong fong]

Thanks for your help to solve my earlier questions. I need to further seek your help to solve following using model:


1) Joseph has some local and foreign stamps in 2 boxes. In Box A, the numbers of local and foreign stamps are in the ratio 3: 4. In Box B, the number of local stamps is twice the number of foreign stamps. Joseph transfers half of the foreign stamps from Box A to Box B. The numbers of stamps in Box A become 105 and the ratio of the number of local stamps to the number of foreign stamps in Box B becomes 6:5.
a) How many foreign stamps have been transferred from Box A to Box B?
b) What is the number of stamps in Box B at first?

2) Ravi had a total of 80 pieces of $10 notes and $50 notes. He used ½ of his $10 notes and withdrew another four pieces of $50 notes from the bank. After which, the number of $50 notes he had was 2/5 the number of $10 notes. Find the total value of the 80 pieces of notes he had at first.

3) 2/9 of Rani’s balloons were red and the rest were green. She gave away 15 green balloons and bought another 25 red balloons. She then had the same number of red and green balloons. How may green balloons did she have at first?

Thanks in advance.

[MathIzzzFun]

happyheart:

MathIzzzFun:

Q) If Jeremy gives 15 stickers to Ramesh, he will have four times as many stickers as Ramesh. If Ramesh gives 5 stickers to Jeremy, the ratio of Jeremy's stickers to Ramesh stickers would be 14:1. How many stickers does Jeremy have?

other than model method, you can use cross-multiply/unit & parts method,
here's a solution using cross-multiply method.. here are some other solutions using the cross-multiply method in this forum:

http://tinyurl.com/ksp-Xmultiply

...If Jeremy gives 15 stickers to Ramesh,
Jeremy's stickers : Ramesh's stickers --> 4u : 1u

At first, Jeremy's stickers : Ramesh stickers --> 4u + 15 : 1u - 15 ** add the 15 stickers to Jeremy's and remove 15 from Ramesh's

If Ramesh gives 5 stickers to Jeremy,
Jeremy's stickers : Ramesh's stickers --> 4u+15 +5 : 1u-15 -5
--> 4u + 20 : 1u - 20
= 14 : 1

cross-multiply
4u + 20 = 14u - 280
10u --> 300
1u --> 30

Jeremy's stickers --> 4 x 30 + 15 = 135

if you need the solution model, I will try to post it when I find some time.

cheers.

I can understand the soulution but confused as to why you cross multiply? How to I explain to DS? Thanks.

4u + 20 : 1u - 20
= 14 : 1
--> 14 parts : 1 part

Left hand side --> 14 parts,
Right hand side --> 1 part ... equalize the parts...

1 part --> 1u - 20
14 parts --> 14u - 280

So, 4u + 20 = 14u - 280

here's another example, using model to illustrate the cross-multiply process - http://tinyurl.com/mathizzzfun-Xmultiply/

cheers.