Jack's Marbles

Question

Jack has m marbles and the number of marbles that I have is 3 times that of Jack's. If we have a total of 2(m+13) marbles, how many marbles does Jack have?

Answer 1

Jack = m marbles

 

Me = 3m marbles

 

Total marbles →   4m = 2(m + 13)

 

 Distribute           4m = 2m + 26

 

                         -2m   -2m

 

                           2m = 26

 

                        2m/2 = 26/2

 

                              m = 13   The number of marbles Jack has

 

                             3m = 39   The number of marbles I have

 

So together we have 52 marbles.

 

 

CHECK

 

Total marbles = 2(m + 13) = 2(13 + 13) = 2(26) = 52 marbles   √

Answer 2

Hi Harrison, let m be the number of marbles Jack has. Then I have 3m marbles. We know the total number of marbles, 2(m + 13).

 

Equation:

m + 3m = 2 * (m + 13)

 

4m = 2m + 26

 

Subtract 2m from both sides:

 

2m = 26

 

Divide both sides by 2:

 

m = 13

 

Solution:

 

Jack has 13 marbles.

 

I have 2 * (13 + 13), or 56 marbles.

 

Check:

 

13 + 3 * 13 = 2 * (13 + 13)

 

13 + 39 = 2 * 25

 

52 = 52, values check.

 

Questions?

Answer 3

Since the total number of marbles is 2(m+13) set up an equation adding Jack's m marbles to the 3 times m marbles to get 2(m+13).  Therefore, the equation is m + 3m = 2(m+13).  Let's simplify the left side by adding m + 3m to get 4m, so now we have 4m = 2(m+13).  On the right side we can distribute the 2 to simplify the equation even more to 4m = 2m + 26.  Subtract 2m from each side of the equation to get 2m = 26.  Now to finish the equation divide both sides of the equation by 2.  The result is m = 13, so Jack has 13 marbles.