Anglo Chinese School 2004 PSLE Math Prelim Question

The ratio of the number of marbles received by John and Peter was 4:7 respectively. The ratio of the number of marbles received by Peter and Sam was 9:5. John gave 1/12 of his marbles to Sam. Peter gave 1/9 of his marble to Sam. Eventually, Sam had 135 marbles.

(a)Find the ratio of the number of John’s marbles to Sam’s marbles at first.
(b)Find the total number of marbles received by the 3 boys.


Solution

Q(a)


Answer: The ratio of the number of marbles to Sam’s is 36:35



Q(b)

John ----- 36 units
Peter ----- 63 units
Sam ----- 35 units

John gave 1/12 to Sam
Peter gave 1/9 to Sam
Eventually, Sam had 135 marbles

John ----- 1/12 x 36 units = 3 units to Sam
Peter ----- 1/9 x 63 units = 7 units to Sam

Sam eventually had ----- 35 units + 3 units + 7 units = 45 units

45 units ----- 135 marbles
1 unit ----- 135/45 = 3 marbles


Total number of marbles received by 3 boys

(John) 36 units + (Peter) 63 units + (Sam) 35 units
= 134 units total

134 units ----- 134 x 3 marbles = 402 marbles altogether.

Answer: The boys received 402 marbles altogether.