Question

There are 73 red, blue and green marbles in a jar. There are twice as many red marbles as blue marbles. There are 19 more marbles than green marbles. How many green marbles are there?

Answer 1

One strategy is to guess a value of the number of green marbles and work backwards to see if the total of green, blue, and red marbles becomes 73.

Suppose:

green = 1

Then

blue = 19 + greeen = 20

red = 2(blue) = 2(20) = 40

This makes for:

green + blue + red = 61

But we need 73 marbles, so we need a larger guess. After working out that 2 and 3 do not work, you will get to green = 4 which does work.

green = 4

blue = 19 + 4 = 23

red = 2(23) = 46

green + blue + red = 73

So there are 4 green marbles.

This trial and error method is not really all that different from the algebra solution.

green = g

blue = b = g + 19

red = 2b = 2(g + 19) = 2g + 38

So then:

g + (g + 19) + 2g + 38 = 73

4g = 16

g = 4

The advantage of algebra is it can be more efficient than trial and error, and it proves there is a single solution. However algebra does involve more careful attention to detail to work through the symbolic manipulation in the intermediary steps.

This is not a particularly challenging problem, but given that students and parents found it baffling, we definitely need additional ways for people to practice and understand mathematics.

Answer 2

Answer

54 green marbles .

Explanation

There are 73 marbles in the jar .

Let the number of blue marbles be x .

This means that the number of red marbles is 2 x since the red marbles are twice as more as the blue marbles .

There are 19 more marbles other than the green marbles .

Hence there are ( 73 - 19 ) green marbles .

There are 54 green marbles .

EXTRA INFO :

Since the number of marbles other than green is 19 , this means that :

red marbles + blue marbles = 19 .

2 x + x = 19

⇒ 3 x = 19

⇒ x = 19/3 which is not an integer .

There may be something wrong with the question . However the number of green marbles are valid.