number of marbles in jars

Question

there are two red jars of marbles and one jar of blue marbles.  Jars of the same color of marbles contain the same number of marbles in them.  there are 35 total marbles.  The difference between the number of marbles in a red jar and the number in a blue jar is 4.   Find the number of marbles in each jar.

Answer 1

x=# of marbles in a red jar

y=# of marbles in a blue jar

x+x+y=35

x-y=4

2x+y=35

add the equations

3x=39

x=39/3

x=13 marbles in each red jar

13-y=4

13-4=y

9=y

there are 9 marbles in the blue jar

 

 

Answer 2

Here's what we know:

2r + b = 35 (total number of marbles is the three jars; 2 are red evenly split, other blue)

r - b = 4 (the difference between two color jars is 4 marbles)

r = b + 4 (isolating a variable for substitution)

 

2(b + 4) + b = 35

Distribute:

2b + 8 + b = 35

Simplify:

3b + 8 = 35

Isolate b:

3b = 27

b = 9

Solve for r:

r = 9 + 4

r = 13

Check

13 * 2 + 9 = 35

26 + 9 = 35

35 = 35

 

Now just to make sure it can or cannot work with the reversal of difference with the marbles, we'll switch which is being subtracted and go through the process again:

b - r = 4

b = r + 4

 

2r + (r + 4) = 35

3r + 4 = 35

3r = 31

 

31 isn't evenly divisible by 3, so we only have the original solution of 13 reds in each jar and 9 blue marbles in its own jar.