The width of the walkway is 8m
Step-by-step explanation:
Given that,
Dimensions of pool is 22 x 10
The area of the pool including the walkway = 540 sq. meter
The area of the pool = 22 x 10
= 220 sq. meter
The area of the walkway= 540 - 220
= 320 sq. meter
The area of the pool with the walkway= 540 sq. meter
Let the width of the walkway be 'w'
Area = (22+w) (10+w)
540 = 220+22w+10w+(w^2)
540-220 = 32w + (w^2)
320 = (w^2) + 32w
(w^2) +32w = 320
(w^2) +32w - 320 = 0
Solving the quadratic equation by splitting the middle term.
(w^2) +40w -8w -320 =0
w(w+40) -8(w+40) =0
(w+40) (w-8) =0
w= 8 (or) -40
The width cannot be negative so the width of the walkway is 8 meter
![a = - 2](https://tex.z-dn.net/?f=a%20%3D%20%20-%202)
Step-by-step explanation:
1) Subtract 8 from both sides.
![- 3a = 14 - 8](https://tex.z-dn.net/?f=%20-%203a%20%3D%2014%20-%208)
2) Simplify 14 - 8 to 6.
![- 3a = 6](https://tex.z-dn.net/?f=%20-%203a%20%3D%206)
3) Divide both sides by, -3.
![a = - \frac{6}{3}](https://tex.z-dn.net/?f=a%20%3D%20-%20%20%20%5Cfrac%7B6%7D%7B3%7D%20)
4) Simplify 6/3 to 2.
![a = - 2](https://tex.z-dn.net/?f=a%20%3D%20%20-%202)
Therefor, the answer is, a = -2.
Each roll has 100 tickets, and 32 were bought.
Multiply 32 with 100
32 x 100 = 3200
3200 tickets were bought in all
hope this helps