So what we have to do to solve this problem is to write down those values in 2 equations (one that represents what you sold and the other what your friend sold) compare them and find how much each ticket is worth.
First equation : 11x + 8y = 158
Where x = how much each adult ticket is
and y = how much each student ticket is
The second equation is : 5x + 17y = 152
Using the method of substitution , we can compare each equation side by side:
11x + 8y = 158
5x + 17y = 152
Now we need to set one of the variables of both equations so they are equal:
11(5)x + 8(5) = 158(5)
5(11)x + 17(11)x = 152(11)
55x + 40y = 790
55x + 187y = 1672
Then we subtract the second equation by the first one
55x-55x + 187y - 40y = 1672 - 790
147y = 882
y = 6
The we apply y to one of the equations to discover x :
11x + 8y = 158
11x + 8(6) = 158
11x + 48 = 158
11x = 110
x = 10
So the awnser is :
Each adult ticket (x) is $10
And each student ticket (y) is $8
I hope you understood my explanation,
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Step-by-step explanation:
Cone Volume = 1/3 ×( π r² h) h = 2 × diameter = 2 × 2 × r
Cone Volume = 1/3 ×( π r² h) h = 2 × diameter diameter = 2r
= 2 × (2 × r)
= 4r
Cone Volume = 1/3 ×( π r² 4r)
= (4 π r³ / 3)
The area of the triangle as a function of x is A = 3x^2/[2(x -5)] and the domain is x > 5
<h3>Write the area A of the triangle as a function of x</h3>
From the figure, we have the following points:
(0,y), (5,3), and (x,0)
Next, we calculate the slopes between the points.
This is calculated as follows:
- Slope between (0,y) and (5,3) = [y - 3]/[0 - 5] = [3 - y]/5
- Slope between (5,3) and (x,0) = [3 - 0]/[5 - x] = 3/[5 - x]
The slopes are equal.
So, we have:
[3 - y]/5 = 3/[5 - x]
Cross multiply
(3 - y)(5 -x) = 15
Divide by 5 - x
(3 - y) = 15/(5 -x)
This gives
y = 3 - 15/(5 -x)
This gives
y = [15- 3x - 15]/[5 - x]
Evaluate
y = 3x/(x - 5)
The area is calculated as:
Area = 1/2 * xy
So, we have:
Area = 1/2 * x * 3x/(x - 5)
Evaluate
Area = 3x^2/[2(x -5)]
Hence, the area of the triangle as a function of x is A = 3x^2/[2(x -5)]
<h3>
The domain of the function</h3>
We have:
A = 3x^2/[2(x -5)]
Set the denominator > 0
2(x - 5) > 0
Divide by 2
x - 5 > 0
Add 5 to the sides
x > 5
Hence, the domain is x > 5
Read more about domains at:
brainly.com/question/2428614
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