Q&A - PSLE Math

[Dharma]

AnnT2009:

Please help,



Q2 Mr Tan bought three times as many badges as toy cars and spent $144 in total. He spent $84 more on toy cars than on badges. Given that a toy car cost $10.40 more than a badge. What is the cost of a badge?
Ans:$1

TIA.

Qty
Badges : 3 units
Toy Cars : 1 unit

Unit Price
Badges : 1 part
Toy car : 1 part + $10.40

Total Value
Badges : (3 units x 1 part)
Toy car : 1 unit x (1 part +$10.40)

(4 units x 1 part) + (1 unit x $10.40) = $144 ------- Eqn 1

(1 unit x $10.40) - (2 units x 1 part) = $84
(2 units x $10.40) - (4 units x 1 part) = $ 168 -------- Eqn 2

Eqn 1 + Eqn 2
(3 units x $10.40) = $ 312
1 unit = 10

40 x 1 part = $144 - $104
1 part = 1

1 part - unit price of badge = $1

[Drdj]

Dear all,


Please assist me with these questions

1. See diagram attached

2. Adrian and Bob started driving at the same time. Adrian takes 6 hours to complete his journey, Bob takes 9 hours to complete his journey.
After 3 hours, both men are left with the same distance to travel.
What is the ratio of Bob's to Adrian's distance ?

3. A, B, C, D share in a gift equally. D forgot to bring his share, so the rest paid for him first. Cindy paid 3/5 of (A+B)'s share. B paid $10 more than A. The next day, Danny returned $24 to C. How much did D return to A and B?

Many, many thanks in advance

Dharma:

AnnT2009:

Please help,


Q2 Mr Tan bought three times as many badges as toy cars and spent $144 in total. He spent $84 more on toy cars than on badges. Given that a toy car cost $10.40 more than a badge. What is the cost of a badge?
Ans:$1

TIA.

Qty
Badges : 3 units
Toy Cars : 1 unit

Unit Price
Badges : 1 part
Toy car : 1 part + $10.40

Total Value
Badges : (3 units x 1 part)
Toy car : 1 unit x (1 part +$10.40)

(4 units x 1 part) + (1 unit x $10.40) = $144 ------- Eqn 1

(1 unit x $10.40) - (2 units x 1 part) = $84
(2 units x $10.40) - (4 units x 1 part) = $ 168 -------- Eqn 2

Eqn 1 + Eqn 2
(3 units x $10.40) = $ 312
1 unit = 10

40 x 1 part = $144 - $104
1 part = 1

1 part - unit price of badge = $1

http://www.postimage.org/

[Dharma]

Hi Drdj


Q1. Missing info in qn …is it triangle CEA or CED?

Q2

Total dist travelled :
Adr - 6 x Speed of A
Bob - 9 x Speed of B

After 3 hrs
Adr travelled - 3x Speed of A
Bob travelled - 3 x Speed of B

Both left w/ same dist to travel after 3 hrs

3 x Speed of A = 6 X Speed of B
Speed of A = 2 X Speed of B

Total distance travelled
Adr - 6 x 2 x Speed of B
Bob - 9 x Speed of B

Ratio of distance travelled - A:B = 12 : 9 = 4:3

[Vanilla Cake]

Drdj:

http://www.postimage.org/

I take your missing info on the area of triangle as CED.
Draw a dotted line to cut through E and label X on the left side and Y on the right side.
Area of rectangle ABXY-> 80 x 2 = 160 cm2
Area of rectangle XYDC-> 60 % of the rectangle ABCD
40%-> 160 cm2
100%->400 cm2
Area of rectangle ABCD is 400 cm2
[quote]Adrian and Bob started driving at the same time. Adrian takes 6 hours to complete his journey, Bob takes 9 hours to complete his journey.After 3 hours, both men are left with the same distance to travel.
What is the ratio of Bob's to Adrian's distance ?[/quote]Adrian
6 h-> 1 whole journey
3 h-> 1/2 journey
Remaining distance -> 1/2 journey = 2/4 journey

Bob
9 h -> 1 whole journey
3 h-> 1/3 journey
Remaining distance -> 2/3 journey

Ratio of Bob's to Adrian's distance -> 3 : 4

[Vanilla Cake]

A, B, C, D share in a gift equally. D forgot to bring his share, so the rest paid for him first. Cindy paid 3/5 of (A+B)'s share. B paid $10 more than A. The next day, Danny returned $24 to C. How much did D return to A and B?


Draw a model:
4 equal blocks and divide into 5 parts for A, B, C and D.
Amount of money paid in units for C-> 3/5x(5+5)= 6 units
Amount of money C paid in units for D-> 6-5 = 1 unit
So, 1 unit-> $24
4 units-> $ 96
Amount of money that D returned to A and B was $ 96

[Dharma]

[quote="Drdj"]Dear all,


3. A, B, C, D share in a gift equally. D forgot to bring his share, so the rest paid for him first. Cindy paid 3/5 of (A+B)'s share. B paid $10 more than A. The next day, Danny returned $24 to C. How much did D return to A and B?

A paid - 5units
B paid - 5 units + $10
C paid - 3/5x(10units + $10) = 6units + $6

Total paid by A,B and C = 16units + $16

If shared equally , each should bear = 4units +$4

(6units + $6) - (4 units +$4) = $24
2 units +$2 = $24
2 units = $22
1 unit = $11

D must return to A = (5 units) - (4 units +$4) = $7
D must return to B = (5 units +$10) - (4 units +$4) = $17

[Dharma]

http://www.postimage.org/[/quote]


Alternatively, if area of CED = 30% of area of ABCD

Then, area of AEB must be 20% of area of ABCD
# Area of AEB + Area of CED = Area of AEC + Area of BED

20% - 80cm2
100% - 400cm2

Area of ABCD - 400cm2

[Drdj]

Thank you so much, Dharma and Vanilla Cake Your wonderful response is very much appreciated !!


A question for your solution

\"Alternatively, if area of CED = 30% of area of ABCD
Then, area of AEB must be 20% of area of ABCD\"
How do you know Triangle AEC = Triangle BEC ? (by proportion) ?

Similarly for your 1st solution, when you draw a line through, we assume the 2 triangles constitute the area of Triangle AEB.

Apologies for the trouble

Dharma:

http://www.postimage.org/

Alternatively, if area of CED = 30% of area of ABCD

Then, area of AEB must be 20% of area of ABCD
# Area of AEB + Area of CED = Area of AEC + Area of BED

20% - 80cm2
100% - 400cm2

Area of ABCD - 400cm2[/quote]

[Dharma]

Dear Drdj,


There isn’t any triangle BEC … it’s just that areas triangle AEC and BED add up 50% of the area of ABCD …cause they share a common base and the perpendicular dist is the breath of the rect.

Similarly triang. AEB and CED, their areas also add up to the remaining 50% of area of rect. ABCD

[small]

Dharma:

AnnT2009:

Please help,



Q2 Mr Tan bought three times as many badges as toy cars and spent $144 in total. He spent $84 more on toy cars than on badges. Given that a toy car cost $10.40 more than a badge. What is the cost of a badge?
Ans:$1

TIA.

Qty
Badges : 3 units
Toy Cars : 1 unit

Unit Price
Badges : 1 part
Toy car : 1 part + $10.40

Total Value
Badges : (3 units x 1 part)
Toy car : 1 unit x (1 part +$10.40)

(4 units x 1 part) + (1 unit x $10.40) = $144 ------- Eqn 1

(1 unit x $10.40) - (2 units x 1 part) = $84
(2 units x $10.40) - (4 units x 1 part) = $ 168 -------- Eqn 2

Eqn 1 + Eqn 2
(3 units x $10.40) = $ 312
1 unit = 10

40 x 1 part = $144 - $104
1 part = 1

1 part - unit price of badge = $1

Hi Dharma,

Much appreciated if you can elaborate on how to get this:

(1 unit x $10.40) - (2 units x 1 part) = $84

Thanks in advance.