Q&A - PSLE Math

[tianzhu]

pensiveowl:

Could someone pls help with this one as well - thanks


The ratio of the number of green marbles to the red marbles in a box is 6 : 5. After 60 green marbles and 60 red marbles were removed from the box. the ratio of the number of green marbles to red marbles became 9 : 7. How many red marbles were there in the box at first?

Hi

The number of green marbles and red marbles removed from the box are the same.

Hence the difference between the number of green marbles and red marbles stay the same before and after.

At first.
Green: Red ------ 6:5 -------12:10
Difference ----- 1 ------ 2

In the end
Green: Red ------ 9:7
Difference ----- 2

Make the difference the same.

3 units ------ 60
1 unit ------ 20

At first, red marbles -------10*20 -------200

Best wishes

[MathIzzzFun]

pensiveowl:

Could someone pls help with this one as well - thanks


The ratio of the number of green marbles to the red marbles in a box is 6 : 5. After 60 green marbles and 60 red marbles were removed from the box. the ratio of the number of green marbles to red marbles became 9 : 7. How many red marbles were there in the box at first?

Hi

the two questions are similar, but for q2, the concept of \"same gap\" can be applied to solve.

q1. Mr Ho and Mrs Lee took part in a chess competition. Mr Ho played against 1/3 as many men as women. Mrs Lee played against 2/5 as many men as women. How many women took part in the chess competition?

Mr Ho played 1/3 as many men as women --> men : women = 1u : 3u
..total number of men = 1u + 1

Mrs Ho played 2/5 as many men as women
--> men : women = 1u + 1 : 3u -1 = 2 : 5

cross-multiply: 5u+5 = 6u -2, 1u = 7

Number of men = 1u + 1 = 8
Number of women = 3u = 21

q2. The ratio of the number of green marbles to the red marbles in a box is 6 : 5. After 60 green marbles and 60 red marbles were removed from the box. the ratio of the number of green marbles to red marbles became 9 : 7. How many red marbles were there in the box at first?

at first, green : red = 6u : 5u
in the end, green : red = 6u - 60 : 5u - 60 = 9 : 7
so, 42u - 420 = 45u - 540, 3u = 120, 1u = 40

At first, red marbles = 5u = 200

using \"same gap/difference\":

in the end, green : red = 9u : 7u (gap 2u)
at first, green : red = 6 : 5 = 12u : 10 u (gap 2u)
so 3u = 60, 1u = 20

Number of red marbles at first = 10u = 200

cheers.

[pensiveowl]

tianzhu:

pensiveowl:

Could someone pls help with this one as well - thanks


The ratio of the number of green marbles to the red marbles in a box is 6 : 5. After 60 green marbles and 60 red marbles were removed from the box. the ratio of the number of green marbles to red marbles became 9 : 7. How many red marbles were there in the box at first?

Hi

The number of green marbles and red marbles removed from the box are the same.

Hence the difference between the number of green marbles and red marbles stay the same before and after.

At first.
Green: Red ------ 6:5 -------12:10
Difference ----- 1 ------ 2

In the end
Green: Red ------ 9:7
Difference ----- 2

Make the difference the same.

3 units ------ 60
1 unit ------ 20

At first, red marbles -------10*20 -------200

Best wishes

Thanks Tianzhu!

[TT2]

Hi, how to do this qn?


Given that p:(q+r)=1:3, r:(q+s)=1:2 and p:s=2:5.
(a) find p:q:r:s
(b) find (r+q):(p+s)

Thank you

[TT2]

Hi, need help on another speed qn…


Ahmad started traveling from town P towards town Q at 7am. After traveling for some time, he passed Steve who was traveling at an average speed of 80 km/h on the opposite direction. After traveling for another 2 hrs, Ahmad reached town Q while Steve was still 40km away from town P.

(a) if Ahmad reached town Q at 1pm, what was his average speed?
(b) if Steve started his journey from town Q, at what time did he leave town Q?

Thank you.

[tianzhu]

TT2:

Hi, how to do this qn?


Given that p:(q+r)=1:3, r:(q+s)=1:2 and p:s=2:5.
(a) find p:q:r:s
(b) find (r+q):(p+s)

Thank you

Hi

Please refer to Vanilla Cake’s post @ page 432.

http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=69&t=280&start=4310

Best wishes

[TT2]

tianzhu:

TT2:

Hi, how to do this qn?


Given that p:(q+r)=1:3, r:(q+s)=1:2 and p:s=2:5.
(a) find p:q:r:s
(b) find (r+q):(p+s)

Thank you

Hi

Please refer to Vanilla Cake’s post @ page 432.

http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=69&t=280&start=4310

Best wishes

Got it. Thank you, tianzhu

[MathIzzzFun]

TT2:

Hi, need help on another speed qn...


Ahmad started traveling from town P towards town Q at 7am. After traveling for some time, he passed Steve who was traveling at an average speed of 80 km/h on the opposite direction. After traveling for another 2 hrs, Ahmad reached town Q while Steve was still 40km away from town P.

(a) if Ahmad reached town Q at 1pm, what was his average speed?
(b) if Steve started his journey from town Q, at what time did he leave town Q?

Thank you.

Hi

Draw a diagram to show the journey - name the meeting point X.
From X, after Steve travelled for 2h, he was 40 km from P.
So, distance PX = 40 km + 2 x 80 km/h = 200 km

Ahmad reached Town Q at 1pm, so total journey time = 6h, time taken to travel from Town P to meeting point X = 4h.

So, Ahmad's speed = 200km/4 h = 50 km/h

Steve met Ahmad at 7am + 4h = 11am
Time taken for Steve to travel from Town Q to meeting point X
= 50/80 x 2h = 1h 15min

He left Town Q at (11am - 1h 15min) = 9.45 am

cheers.

cheers.

[pensiveowl]

MathIzzzFun:

pensiveowl:

Could someone pls help with this one as well - thanks


The ratio of the number of green marbles to the red marbles in a box is 6 : 5. After 60 green marbles and 60 red marbles were removed from the box. the ratio of the number of green marbles to red marbles became 9 : 7. How many red marbles were there in the box at first?

Hi

the two questions are similar, but for q2, the concept of \"same gap\" can be applied to solve.

q1. Mr Ho and Mrs Lee took part in a chess competition. Mr Ho played against 1/3 as many men as women. Mrs Lee played against 2/5 as many men as women. How many women took part in the chess competition?

Mr Ho played 1/3 as many men as women --> men : women = 1u : 3u
..total number of men = 1u + 1

Mrs Ho played 2/5 as many men as women
--> men : women = 1u + 1 : 3u -1 = 2 : 5

cross-multiply: 5u+5 = 6u -2, 1u = 7

Number of men = 1u + 1 = 8
Number of women = 3u = 21

q2. The ratio of the number of green marbles to the red marbles in a box is 6 : 5. After 60 green marbles and 60 red marbles were removed from the box. the ratio of the number of green marbles to red marbles became 9 : 7. How many red marbles were there in the box at first?

at first, green : red = 6u : 5u
in the end, green : red = 6u - 60 : 5u - 60 = 9 : 7
so, 42u - 420 = 45u - 540, 3u = 120, 1u = 40

At first, red marbles = 5u = 200

using \"same gap/difference\":

in the end, green : red = 9u : 7u (gap 2u)
at first, green : red = 6 : 5 = 12u : 10 u (gap 2u)
so 3u = 60, 1u = 20

Number of red marbles at first = 10u = 200

cheers.

Thanks MathIzzzFun!

[TT2]

MathIzzzFun:

TT2:

Hi, need help on another speed qn...


Ahmad started traveling from town P towards town Q at 7am. After traveling for some time, he passed Steve who was traveling at an average speed of 80 km/h on the opposite direction. After traveling for another 2 hrs, Ahmad reached town Q while Steve was still 40km away from town P.

(a) if Ahmad reached town Q at 1pm, what was his average speed?
(b) if Steve started his journey from town Q, at what time did he leave town Q?

Thank you.

Hi

Draw a diagram to show the journey - name the meeting point X.
From X, after Steve travelled for 2h, he was 40 km from P.
So, distance PX = 40 km + 2 x 80 km/h = 200 km

Ahmad reached Town Q at 1pm, so total journey time = 6h, time taken to travel from Town P to meeting point X = 4h.

So, Ahmad's speed = 200km/4 h = 50 km/h

Steve met Ahmad at 7am + 4h = 11am
Time taken for Steve to travel from Town Q to meeting point X
= 50/80 x 2h = 1h 15min

He left Town Q at (11am - 1h 15min) = 9.45 am

cheers.

cheers.

:thankyou: MathIzzzfun