How do I write the equation for this?

Question

John was on his way to a marble tournament when he met rose. Johns bag was heavy so he have 1/2 to rose plus 2 more. Then he might sam and gave her 1/4 of his remaining plus 5. Finally he saw jake and gave him 1/2 of the marbles he had left. When john arrived he had 2 marbles how many did he start with?

Answer 1

This question is best done in reverse order.

 

At the end John has 2 marbles and Jake has 2 marbles. 

 

Since each boy had 1/2 of the marbles Jon had before he met Jake then before John met Jake, John had 4 marbles.

 

If John gave Sam 1/4 of his total marbles, plus 5 we must do the following:

Above John had 4 marbles, so we add the 5 to get 9 marbles.  If 9 marbles is 3/4 of what he had before he met Sam then 9/X = 3/4 ... or 36 = 3X solve for X = 12

So before he met Sam, John had 12 marbles

 

If John gave Rose 1/2 of his total marbles, plus 2 more we must do the following:

Above John had 12 marbles, so we add the 2 to get 14 marbles. If 14 marbles is 1/2 of what he had before he met Rose then 14/Y = 1/2 ... or 28 = Y
So before he met Rose, John had 28 marbles.

 

Doc L.

Answer 2

Margaret, Let us work with fractions and with John is left with. After giving to Rose, John is left with (1/2) x - 2. After giving to Sam, John is left with (3/4)(1/2) x - (3/4) (2) - 5 = (3/8) x - (3/2) - 5. After giving to Jake, John is left with (1/2)(3/8) x - (1/2)(3/2) - (5/2) = (3/16) x - (3/4) -(5/2) = (3/16) x - (13/4). This quantity equals 2. Hence the required equation is (3/16) x -(13/4) = 2. (3/16) x = (21/4). x = 28.

Answer 3

First, you should write the question in proper English.....

 

Second. the answer is 28 -- just work it backwards.   He had 4 marbles when he met Jake;   12 when he met Sam (giving him 3+5=8);  and 28 when he started, before giving Rose 16 marbles (14+2).

Answer 4

Let x = the number of marbles that John started with

 

He gave 1/2 plus 2 of his marbles to Rose, so the number he had left was:

 

(1/2)x - 2

 

He gave Sam 1/4 of his remaining marbles plus 5, so the number he had left was:

 

(3/4)((1/2)x-2)) - 5 = (3/8)x - (3/2) - 5 = (3/8)x - 13/2

 

He gave Jake 1/2 of what he had left:

 

(1/2)((3/8)x - 13/2) = (3/16)x - (13/4)

 

John had 2 marbles left so:

 

(3/16)x - (13/4) = 2 marbles

 

(3/16)x = 21/4

 

x =(16/3)*(21/4)

 

x = 28