ACS Primary 2010 SA1 Math Paper 2 Q16

Mr Wu had some badges and decided to give them to his two sons, Sean and Matthew. Mr Wu gave 1/3 of the badges and 8 more badges to Sean. He then gave 3/4 of the remainder to Matthew but took back 2 badges. Mr Wu was left with 26 badges. How many badges did Mr Wu have at first?

Solution

Assume all badges --> 1 unit

Mr Wu was left with,

----- 1/4 of Remainder + 2

----- 1/4 x (2/3 unit - 8) + 2

= (1/6 unit - 2) + 2

= 1/6 unit - 2 + 2

= 1/6 unit

1/6 unit --> 26 badges

1 unit ----- 26 divided by 1/6
= 26 x 6
= 156

Answer: 156 badges

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ACS Primary 2010 SA1 Math Paper 2 Q15

Both Joanne and Joseph had an equal amount of money at first. Every month, Joanne spent $850 and Joseph spent $912. After a few months, Joanne was left with $1550 while Joseph had 4/5 as much as Joanne. How much money did Joseph have at first?

Solution

Every month,
Joanne spends $850
Joseph spends $912
Difference every month
--> $912 - $850 = $62


After a few months, Joseph had 4/5 as much as Joanne,

5 units ----- $1550
1 unit ------ $1550 divided by 5 = $310
($310 is the difference between Joanne and Joseph after a certain number of months)


Number of months to achieve the $310 difference,
$310 divided by $62 = 5 (mths)
It also takes 5 months for Joseph to have 4/5 as much as Joanne.


Amount Joseph has at first,
Joseph ------ 4 units + (5 mths x $912 spent per mth)
----- (4 x $310) + (5 x $912)
= $1240 + $4560
= $5800

Answer: $5800


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Another Problem Sum from a reader

Received another question from a reader.
Can anyone help this reader out

Question:
Mrs tan bought 4 times as many toys as teddy bears . She spent $1750 altogether . A toy gun cost $10 less than a teddy bear . The total cost of toy guns was $490 more than the total cost of teddy bears .
(a) How much did Mrs tan spend on the teddy bears?

(B) How much did one teddy bear cost ?

ACS Primary 2010 SA1 Math Paper 2 Q14

Tony and Charles took part in a car race. Tony drove at a speed of 90km/h. Both of them did not change their speed throughout the race. When Charles had covered 1/3 the distance, Tony was 15 km in front of him. Tony reached the finishing line at 9.35 a.m. At what time did Charles recah the finishing line?

Solution

* For every 1/3 of the race Charles covered, Tony was 15 km ahead. When Charles completed the whole race, Tony would have been 3 x 15km = 45km ahead of Charles, if we assume Tony continued to travel beyond the finishing line.

Time = 45 km divided 90 km/h
= 0.5 hour

Half hour after 9.35 am ------ 10.05 am

Answer: 10.05 am

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ACS Primary 2010 SA1 Math Paper 2 Q12

Weiming had 2/3 as many stickers as Shiyang. After Weiming gave 52 stickers to Shiyang, Weiming had 2/5 as many stickers as Shiyang. How many stickers did Weiming have at first?

Solution

*(x7) and (x5) to give a common total of 35 units for both "At first" and "In the end", since there is no change in the total number of stickers.

Weiming gave
14 units - 10 units ---- 52
4 units ----- 52
1 unit ----- 52 divided by 4 = 13

Weiming at first
14 units x 13 = 182

Answer: 182 stickers

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ACS Primary 2010 SA1 Math Paper 2 Q9

The graph below shows the mass of a container when it is empty and when different combinations of objects X, Y and Z are placed in it.

Solution

Empty container --> 80g
Y + Z ----- 140g - 80g = 60g
X + Z ----- 300g - 80g = 220g
X + Y ----- 340 g - 80g = 260g

Total of all objects
----- 60g + 220g + 260g = 540g

Average ----- 540g divided by 6 = 90g


Answer: 90g

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ACS Primary 2010 SA1 Math Paper 2 Q6

At first, Matthew has twice as many soccer cards as Ivan. Each of them then bought the same number of cards. As a result, both of the now have 160 cards in total. If Matthew now has 30 more cards than Ivan, find the number of cards each of them bought.

Solution

bought + bought ----- 160 - 30 - 30 - 30 = 70
bought ----- 70 divided by 2 = 35


Answer: 35 soccer cards

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