Rosyth Sch 2006 PSLE Math Prelim Q46

At a fun fair, there were 49 more children than women. There were 3/5 as many men as women. Given that the number of women was 25% of the total number of people at the fun fair, how many people were at the fun fair?

Solution

Men ----- 3 units
Women ----- 5 units
Children ----- 5 units + 49
Total ----- 13 units + 49

(Women) 5 units ----- 25%
1 unit ----- 25% divided by 5 = 5%
13 units ----- 13 x 5% = 65%

Remaining 49 people ----- 100% - 65% = 35%
35% ----- 49 people
(35% divided by 7)= 5% ----- (49 divided by 7) = 7
5% ----- 7
(5% x 20) = 100% ----- (7 x 20) = 140
100% ----- 7 x 20 = 140

Answer: There were 140 people at the fair.

Rosyth Sch 2006 PSLE Math Prelim Q45

Ali, Billy and Caven had some cards. Ali would have twice as many cards as Billy if Billy gave 28 cards to Ali. Both Billy and Caven would have the same number of cards if Caven gave 84 cards to Billy. Given that Caven had 112 more cards than Ali at the beginning, find the number of cards each of them had at the beginning.

Solution

Ali ----- 2 units – 28 (at first)
Billy ----- 1 unit + 28 (at first)
Caven ----- 1 unit + 28 + 84 + 84 (at first)

At first,
(Caven) – (Ali) ---- 112
(1 unit + 28 + 84 + 84) – (2 units – 28) ----- 112
(1 unit + 196) – (2 units – 28) ----- 112
224 – 1 unit ----- 112
224 – 112 ----- 1 unit
1 unit ---- 112

Ali at first
(2 x 112) – 28 = 196

Billy at first
(112) + 28 = 140

Caven at first
(112) + 28 + 84 + 84 = 308

Answer: Ali had 196, Billy had 140 and Caven had 308