Answer:
The answer to your questions is: 25 new teachers
Step-by-step explanation:
Data
# of students = 2000
ratio = 3:80 teachers to students
New teachers = ?
Process
I suggest to use rule of three to solve this problem
3 teachers ---------------- 80 students
x ---------------- 2000 students
x = (2000 x 3) / 80 = 75 teachers
Number of initial teachers = 75
The ratio change to 1:20
1 teacher ------------------- 20 students
x ------------------- 2000 students
x = (2000 x 1) / 20
x = 100 teachers
Number of new teachers = 100 - 75 = 25
Answer:
The shadow of the building = 192 ft.
Step-by-step explanation:
∵ There is a proportional relation between the heights of the tree and the building and their shadows
∴ Height tree/height building = shadow tree/shadow building
x = 
= 192 ft ⇒ x is the length of the shadow of the building
The midpoint of the segment:
(4, 7)
x=4 y= -7
N=number of nickels
d=number of dimes
q=number of quarters
example
if n:d=3:8
lets say n=3 and d=8
3*8=8*3
so
8n=3d
slightly confusing but go with it, it migh make sense or it might not
n:d=3:8
8n=3d
d:q=4:5
5d=4q
solve for one of them
solve for nickels in first and quarters in second
8n=3d, n=(3/8)d
5d=4q, (4/5)d=q
5n+10d+25q=690
divide by 5 to make it easeir
n+2d+4q=138
sub (3/8)d for n
sub (4/5)d for q
(3/8)d+2d+5(5/4)d=138
(3/8)d+2d+25/4d=138
3/8+2+25/4=
3/8+16/2+50/8=
69/8
(69/8)d=138
times both sides by 8
69d=1104
divide both sides by 69
d=16
16 dimes
sub back
(5/4)d=q
(5/4)16=q
80/4=q
20=q
(3/8)d=n
(3/8)16=n
48/8=n
6=n
6 nickles
16 dimes
20 quarters
yah
