+0  
 
+1
49
2
avatar

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 marbles 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.

 Nov 4, 2021
 #1
avatar
+1

Ratios can be scaled up or down by multiplication or division.

So for example the ratio 4 : 7 is the same as 8 : 14 (having multiplied by 2), or 12 : 21 ( having multiplied by 3) and so on.

With problems like this, where two ratios are involved, the thing to do is to arrange for two of the components, (in different ratios) to be equal to each other. So, multiply the first ratio by 9 and the second by 7 to arrive at

J : P = 36 : 63, and P : S = 63 : 35.

The two can then be shunted together so J : P : S = 36 : 63 : 35.

The actual number of marbles for each person will then be (for some positive integer k), 36k for John, 63k for Peter and 35k for Sam.

John then gives 3k and Peter gives 7k to Sam.

That means that Sam now has 35k + 3k + 7k = 45k marbles and that has to equal 135, so k = 3, etc. .

 Nov 5, 2021
 #2
avatar+103 
+1

Ratio of marbles of Peter by Sam, P : S = 9 : 5

 

Now,  J : P : S = 36 : 63 : 35

 

 

 

(a)    Ratio of John by Sam : J : S = 36 : 35

 

(b)    Let the number of marbles with John = 36x

                                                           Peter = 63x

                                                           Sam = 35x

 

        When John Gabe 1/12 of his marble to Sam and

        Peter gave 1/9 of his marbles to Sam. Then

        
        marbles with Sam = 35x + (36x * 1/12)

                               

                                                + (63 * 1/9)

                                      = 35x + 3x + 7x

                                      = 45x

 

        According to Question

           45x = 135

          => x = 135/45 = 3

  
      Total marbles + (36x + 63x + 35x) = 134x = 134 * 3

                                                                         = 402

 Nov 6, 2021

8 Online Users

avatar