Which of the values below represents 70 as a percntage of 40
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Taking into account the definition of a system of linear equations, the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.
<h3>System of linear equations</h3>A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
<h3>Amount of ticket sold</h3>In this case, a system of linear equations must be proposed taking into account that:
- "x" is the amount of adult tickets sold.
- "y" is the amount of child tickets sold.
The maximum capacity for seating in a theater is 500 people. If they sold out on a certain showtime, this is represented by x+y=500.
On the other side, the theater sells two types of tickets, adult tickets for $7.25 each and child tickets for $4 each and the made a total of $3,157. This is represented by 7.25x +4y=3157.
So, the system of equations to be solved is
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable x from the first equation you get:
x=500 - y
Substituting this expression in the second equation you get:
7.25× (500 -y) +4y=3157
7.25×500 - 7.25y +4y=3157
3625 - 7.25y +4y=3157
- 7.25y +4y=3157 -3625
-3.25y= -468
y= (-468)÷ (-3.25)
<u><em>y= 144</em></u>
Substituting this value in the expression x=500 - y you get:
x=500 - 144
<u><em>x=356</em></u>
Remembering that "x" is the amount of adult tickets sold and "y" is the amount of child tickets sold, you get that the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.
Learn more about system of equations:
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The coordinates of the point P which divides the line segment AB made by the points A(-7,2) and B(9,-6) is (x,y) = (5,-4)
<h3>What is the coordinate of the point which divides a line segment in a specified ratio?</h3>Suppose that there is a line segment such that a point P(x,y) lying on that line segment
divides the line segment
in m:n, then, the coordinates of the point P is given by:
where we have:
- the coordinate of A is
- and the coordinate of B is
We're given that:
- Coordinate of A is
= (-7,2)
- Coordinate of B is
= (9.-6)
- The point P lies on AB such that AP:BP=3:1 (so m = 3, and n = 1)
Let the coordinate of P be (x,y), then we get the values of x and y as:
Thus, the coordinates of the point P which divides the line segment AB made by the points A(-7,2) and B(9,-6) is (x,y) = (5,-4)
Learn more about a point dividing a line segment in a ratio here:
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