Q&A - PSLE Math

[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.

[MathIzzzFun]

lee tong fong:

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



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.

ratio of red balloons : green balloons
= 2/9 : 7/9
--> 2u : 7u

Bought 25 red balloons & give away 15 green balloons, in the end,
number of red balloons : green balloons
= 2u + 25 : 7u - 15
--> 1 : 1

2u + 25 = 7u - 15
5u --> 40, 1u --> 8

Number of green balloons at first = 8 x 7 =56



cheers.

[MathIzzzFun]

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.


Thanks in advance.

In the end,
number of $50 notes : $10 notes
--> 2u : 5u

At first,
number of $50 notes = 2u - 4 (since 4 pieces of $50 were added)
number of $10 notes = 2 x 5u = 10u

Total number of notes at first --> 2u - 4 + 10u = 12u -4

12u - 4 = 80
1u --> 7

At first,
value of $50 notes --> $50 x (2 x 7 -4) = $500
value of $10 notes --> $10 x 10 x 7 = $700
Total $1200

cheers.

[MathIzzzFun]

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?

Thanks in advance.

For Box B-
at first, local : foreign = 2 : 1 = 6u : 3u --> total 9u
in the end, local : foreign = 6u : 5u

foreign stamps added --> 5u-3u = 2u

since half of foreign stamps in Box A was transferred to Box B,
2u --> half of foreign stamps in Box A
originally, foreign stamps in Box A --> 2u x 2 = 4u

at first, local stamps in Box A : foreign stamps in Box A = 3u : 4u
in the end, local stamps in Box A : foreign stamps in Box A = 3u : 2u --> total 5u

5u --> 105, 1u --> 21

a) foreign stamps transferred from A to B = 2 x 21 = 42
b) total number of stamps in Box B at first = 9 x 21 = 189

cheers.

[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!

Here's the solution using MD... I have the intermediate steps in arriving at the final model..

http://i50.tinypic.com/vzhusx.png\">

cheers.

[lee tong fong]

Thanks for your great help MathIzzzFun and skyed. I have 2 more questions need you to solve if possible use model… Thanks in advance.


1) Jane and Iris had 255 sweet together. Jane had 15 more sweets than Iris. Jane gave away 25% as many sweet as Iris. She was left with twice as many as sweets as Iris.

(a)How many sweets did Iris give away?
(b)How many sweets did Jane have in the end?

2) Sushila went shopping. She spent $588 on 2 dresses, 3 shirts and 2 pairs of
sunglasses. The total amount spent on the dresses was 0.4 of the total amount
spent on the skirts and sunglasses.The total amount spent o the sunglasses was
1/ 3 of the total amount spent on dresses and shirts.

(a)\tHow much did she spend on the 2 pairs of sunglasses?
(b)What was the cost of the third shirt if the average cost of the two shirts was
$88?