Alex has a bag of marbles. Each marble is red or blue, and the ratio of red to blue marbles is 3 : 5. After Alex adds 10 red mar

Question

2 years ago

11

bles to the bag, the ratio of red to blue marbles is 2 : 3. How many blue marbles are in Alex’s bag?

1 answer:

Otrada [13] · Answer 1 · 2023-04-25T15:19:34+03:00

Solving a system of equations we will see that there are 150 blue marbles in the bag

<h3>How many blue marbles are in Alex’s bag?</h3>

We know that initially, the ratio of red to blue marbles is 3:5

This means that if there are 8*n marbles in the bag, there are:

Now, when he adds 10 red marbles, the new ratio is 2:3, this means that if now there are 5*m marbles, we have:

Where we will have two relations, so we have a system of equations:

3*n + 10 = 2*m

8*n + 10 = 5*m

With these two we can find the value of n and m.

To do that, we isolate m in the first equation:

m = (3*n + 10)/2

Now we can replace that in the other equation to get:

8*n + 10 = 5* (3*n + 10)/2

Now we can solve this for n:

2*(8*n + 10) = 5*(3n + 10)

16n + 20 = 15n + 50

n = 50 - 20 = 30

n = 30

And the number of blue marbles is:

5*n = 5*30 = 150

There are 150 blue marbles.

If you want to learn more about systems of equations:

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