Dymin had a lot of boxes ready for moving. She went out and bought seven more boxes. A week later her little brother
destroyed half of them. There are now only 22 boxes left.
How many did she start with?

37 boxes

Step-by-step explanation:

At first, Dymin had some boxes. Let x be the starting number of boxes.

Then, she bought 7 more boxes. Let y be the new number of boxes that she had.

y = x + 7

Next, her little brother destroyed half of them. It means half of y. So, the number of boxes left is

Number of boxes = y/2

The number of the boxes left is 22 boxes. Then, we can use the equation above.

Number of boxes = 22

y/2 = 22

Substitute y = x + 7 into the equation.

(x + 7)/2 = 22

x + 7 = 44

x = 44 - 7

x = 37

Thus, Dymin has 37 boxes at first.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8