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Answer:
number of adults tickets sold = x = 90
number of teachers tickets = y = 45
number of students tickets = z = 145
Step-by-step explanation:
Cost of tickets
Adults = $6
Teachers = $4
Students = $2
Total tickets sold = 280
Total revenue = $1010
Let
x = number of adults tickets
y = number of teachers tickets
z = number of students tickets
x + y + z = 280
6x + 4y + 2z = 1010
If the number of adult tickets sold was twice the number of teacher tickets
x = 2y
Substitute x=2y into the equations
x + y + z = 280
6x + 4y + 2z = 1010
2y + y + z = 280
6(2y) + 4y + 2z = 1010
3y + z = 280
12y + 4y + 2z = 1010
3y + z = 280 (1)
16y + 2z = 1010 (2)
Multiply (1) by 2
6y + 2z = 560 (3)
16y + 2z = 1010
Subtract (3) from (2)
16y - 6y = 1010 - 560
10y = 450
Divide both sides by 10
y = 450/10
= 45
y = 45
Substitute y=45 into (1)
3y + z = 280
3(45) + z = 280
135 + z = 280
z = 280 - 135
= 145
z = 145
Substitute the values of y and z into
x + y + z = 280
x + 45 + 145 = 280
x + 190 = 280
x = 280 - 190
= 90
x = 90
Therefore,
number of adults tickets sold = x = 90
number of teachers tickets = y = 45
number of students tickets = z = 145
Answer:
Step-by-step explanation:
the y= equation shows how... b/c we can just plug y into the 2nd equation and eliminate y and have one variable, x , to solve for :)
Answer:
The new radius r' should be 1.1 times the original planned radius ( rp ).
Step-by-step explanation:
Solution:-
- We will assume the geometry of the pond is modeled as a cylinder with base modeled as a circle with radius ( r ) and the planned height of the ( hp = 6 feet ).
- The volume V of a cylindrical pond is given by:
V = π*r^2*h
- Talisa had planned a depth hp = 6 feet, The planned volume with planned radius ( rp ) was:
Vp = π*rp^2*6
- However, she hit a rock at h' = 5 feet, So what change must he make to the radius of the pond such that she achieves the planned volume of the pond.
V = π*r'^2*h'
Where, r' is the new radius of the pond:
Vp = V
π*rp^2*6 = π*r'^2*5
( r' / rp )^2 = 6 / 5
r' / rp = √6 / 5
r' / rp = 1.09544
r' = 1.1*rp
- The new radius r' should be 1.1 times the original planned radius ( rp ).