find the value of x

Question

Dhruv and hemant had 60 marbles altogether,after hemant gave 1/6 of his to dhruv.dhruv has twice as that of hemant.how much dhruv has at first?

Answer 1

d = Dhru's marbles

h = Hemant's marbles

 

d + h = 60

d + h/6 = 2(h - h/6)

 

Let's simplify the 2nd equation:

d + h/6 = 2(5h/6)

d + h/6 = 5h/3       multiply through by 6

6d + h = 10h

6d - 9h = 0

 

We have 2 equations with 2 unknowns to work with:

 

d + h = 60

6d - 9h = 0

We can solve by substitution or elimination.  Let's use elimination.

Multiply 1st by 9 and add equations.

 

9d + 9h = 540

6d - 9h = 0

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15d = 540

d = 36 marbles originally