Question

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

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

### How many blue marbles are in Alex’s bag?

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:
• 3*n red marbles.
• 5*n blue marbles.
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:
• 2*m red marbles
• 3*m blue marbles.
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.