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

Short 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.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions