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If you understand how the equations are set up, then you've gotten through the hardest part. Here are the rest of the steps:
5x/7x = original ratio
3y/2y = new ratio
5x + 3 = 3y
7x - 9 = 2y
I'd try to combine these two equations.
If we multiply 5x + 3 = 3y by 2, we have 6y on the right, and
if we multiply 7x - 9 = 2y by 3, we have 6y on the right.
Our two equations are now:
10x + 6 = 6y
21x - 27 = 6y
Since both are equal to 6y, we can set them equal to each other:
10x + 6 = 21x - 27
33 = 11x
3 = x
We can then plug x=3 back into either equation to find y:
5x + 3 = 3y
5(3) + 3 = 3y
15 + 3 = 3y
18 = 3y
6 = y
Therefore, the number of red pens after the change is 2y, which is 2*6, or 12.
Veritas Help
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