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.