Question

Raul has 56 bouncy balls. He puts three times as many balls into red bags as he puts into green gift bags. If he puts the same number of balls into each bag,how many balls does he put into green bags?

Answer 1

If we divide 56 by 4 we get 14.  Why by4?  So that one number is 3 times the other So he had 14 balls that went into the green bags and 42 (56-14) that went into the red bags.  We could just answer the question and say 14 but I think they want to know how many in each green bag.
14 and 42 don't work because they are not the same number of balls.  What number is a common factor?  7 is,
We could have 2 green bags and split the 14 balls into 2 groups of 7 and with the remaining 42 - put them into 6 red bags of 7 each.
And so the answer to your question is:
7 ball in each bag  = 2 bags are green, and 6 bags are red
                                        14 balls              +    42 balls            = 56 bouncy balls
 

Answer 2

The total number of balls Raul puts into green bags is 14.

Further explanation

To tackle this problem, first we need to define our unknowns:

• The first unknown will be the number of balls Raul puts into each bag, we can call this b. It is to be noted that Raul puts the same number of balls into each bag, whether it's red or green.
• The second and third unknown will be the number of red bags and green bags, we can call them R and G, respectively.

From the problem statement we can obtain 2 conditions:

1. The total number of balls is 56. We can write this as $(R+G) \cdot b = 56$.
2. The total number of balls in the red bags is 3 times as much as the total number of balls on the green bags. Since Raul puts the same number of balls into any bag, this means that there are 3 times as many red bags as green bags. We can write this as $3 \cdot G = R$.

In order to solve for the total number of balls in the green bags, we can substitute the second condition into the first one. By doing so we obtain:

$(R+G) \cdot b = (3 \cdot G + G) \cdot b = 4\cdot G \cdot b= 56$

Simplifying we get that $G \cdot b = 14$, which is the total number of balls on green bags.

It is to be noted that on this problem, it's impossible to find how many balls are in each bag, and how many bags are there. Let's show why:

We got that the total number of balls on green bags is 14, and we also know that b and R are both integer numbers (they have to be integers, we can't put 2 balls and a half on each bag, and we can't have 3.5 green bags). This condition implies that either $b=2$ and $R=7$, or $b=7$ and $R=2$ (both solutions satisfy our problem). Ususally these kind of problems are known as Integer programming problems.

Learn more

• Balls on a pit: https://brainly.com/question/902905
• A similar problem to yours: https://brainly.com/question/12888755

Keywords

System of equations, integer programming