**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.**

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