Hey there! :)
Answer:
$10 balcony
$15 orchestra
Step-by-step explanation:
We can solve for the prices of each seat by creating an algebraic expression:
Let 'x' be the cost of a balcony seat:
and 'x + 5' be the cost of an orchestra seat.
200 of both seats were sold, therefore:
200(x) + 200(x + 5) = 5000
Distribute:
200x + 200x + 1000 = 5000
Combine like terms:
400x + 1000 = 5000
Subtract 1000 from both sides:
400x = 4000
Divide:
x = $10 for the balcony seat.
Substitute this value of x to solve for the cost of an orchestra seat:
(10) + 5 = $15.
Therefore:
$10 balcony
$15 orchestra
Answer:
x=61
Step-by-step explanation:
2x-6+x+3=180
3x-3=180
3x=183
x= 61
Step 1-F.O.I.L.: (-2-2i)(-4-3i)
8+6i+8i+3i^2
We know i^2=-1, so...
8+14i-3
5+14i
Step 2-F.O.I.L. again: (5+14i)(7+8i)
35+40i+98i+112i^2
35+138i-112
-77+138i
Note: "F.O.I.L." stands for "First, Outer, Inner, Last". In other words, distribute the terms of the first binomial to the other, in that order. So, (5+14i)(7+8i) should be done as follows:
5*7=56
5*8i=40i
14i*7=98i
14i*8i=112i^2
Answer: The average age is 7.1 years.
This problem is an example of when we need to take a weighted average. We simply can't just find the average of 5 and 8, because there are different children of each each.
To start, lets multiply the total number of children by their individual ages.
6 x 5 = 30 years
14 x 8 = 112 years
There are 142 years among the 20 years, so divide 142 by 20. This gives us an average age of 7.1 years.
