During the summer, every student became 5% taller. Matt was x before summer, after summer he was 105cm.

Short answer: 100

I assume you want to find x.

We want an equation that says that x is equal to 105cm, minus that 5 percent, because that is his height before the 5% was added. That looks like:

x + 0.05x = 105

(0.05 is 5% in decimal form, which is necessary in equations like this).

x + 0.05x = 1.05x

1.05x = 105.

Isolate x by dividing both sides by 1.05

1.05x / 1.05 = x, 105 / 1.05 = 100

x = 100, so he was 100cm tall before summer

My original answer was 99.75. This is wrong because I used the 5% of 105, which is wrong because in the question it says his original height (which is x) had 5% added to it. So its 5% of x, not 5% of 105. This changes the whole equation.