Answer:
B
Step-by-step explanation:
A proportional relationship is represented by linear function with its linear parameter "b" equal to zero. Since b is equal to zero, the line passes through the origin and the function/relation is proportional.
To verify that we divide the y coordinate over the x coordinate we obtain a constant called k, which is the slope.
For instance:
According to this function we can easily check a proportional relationship among its points:
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:
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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He will use 11 and half cups of olive oil to use with 1 teaspoon of cinnamon.
Step-by-step explanation:
Given,
Olive oil used in recipe = 23 cups
Cinnamon used in recipe = 2 teaspoons
Ratio of cinnamon to olive oil in recipe = 2:23
Cinnamon Leon has = 1 teaspoon
Let x be the olive oil.
Ratio of available cinnamon to olive oil = 1:x
Using proportion;
Ratio of cinnamon to olive oil in recipe :: Ratio of available cinnamon to olive oil
Product of extreme = Product of mean
Dividing both sides by 2;
11.5 can also be written as
He will use 11 and half cups of olive oil to use with 1 teaspoon of cinnamon.
Keywords: ratio, proportion
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