MATHEMATICS HIGH SCHOOL

The John Jay Theater Dept has tickets at $6 for adults, $4 for teachers, and $2 for students. A total of 280 tickets were sold for one showing with a total revenue of $1010. If the number of adult tickets sold was twice the number of teacher tickets, how many of each type of ticket were sold for the showing?

Answers

Answer 1

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

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A local television station sells time slots for programs in 30-minute intervals. If the station operates 24hrs per day, every day of the week, what is the total number of 30-minute time slots the station can sell for tuesday and wednesday?

Answers

The local television station can sell 96 of 30-minute time slots on Tuesday and Wednesday.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
For Tuesday and Wednesday,
The number of minutes = days × hours × minutes.

Now, television stations sell time slots for programs in 30 minutes.
Number of 30-minute slots for days Tuesday and Wednesday

= days × hours × minutes / 30
= 2 × 24 × 60 / 30
= 4×24
= 96 slots

Thus, the local television station can sell 96 slots of 30-minute time slots on Tuesday and Wednesday.

Learn more about models here: brainly.com/question/22591166

#SPJ2

1440 is the answer.

30 minutes times 48 since one day is 24 hours times that by 2 to get 48.

48 times 30 is 1440.

Rachel can make 3 bracelets in an hour. Oliver can make only 2 bracelets in an hour, but he already has completed 5 bracelets. Explain to Rachel how she can use a system of equations to determine when she will have the same number of bracelets as oliver.

Answers

Since rachel makes 3 bracelets an hour, her pinear equstion should be y=3h. 3 represents the rate of change and h represents the number of hours as a variable.
Oliver's linear equation is y=2h+5 because 2 is the rate of chabge and 5 is the b value or the y intercept in a linear equation y=mx+b. To find when both have the same number of bracelets, we find the point of intersection...
2h+5=3h
5=3h-2h
5=h
Therefore in 5 hours, both will have the same amount of bracelets.
Hope this helps;)

Answer:

5 hours and 15 bracelets

Step-by-step explanation:

Rachel makes 3 bracelets per hour so you can set that up as the equation y=3x. Oliver can make 2 bracelets per hour but already has 5 so the equation for that is y=2x+5. These equations form a system of equations because the values for x and y are the same in both equations. This is true because the goal is to find out when Rachel and Oliver swell the same amount of bracelets. In order to solve this, you must set both of the equations equal to each other, this can be done because both equations are equal to y. The equation you now have is 3x = 2x+5. This can be solved as you would solve any linear equation; by isolating the x value then dividing it. In this case, when you do this you subtract 2x from both sides then get x=5 there is not a number multiplied by x so dividing, in this case, is not necessary. Now plug the value of x back into one of the original equations, y=15 should be the answer. Now you know that after 5 hours both Rachel and Oliver will have made 15 bracelets.

Please help me figure this out .

2x+10(340/139)=-18

Answers

Answer:

To solve the equation 2x + 10(340/139) = -18, we can follow these steps:

1. Distribute the 10 to the terms inside the parentheses:

2x + (10 * 340/139) = -18

2x + 3400/139 = -18

2. Combine like terms:

2x + 3400/139 = -18

3. Move the constant term to the other side of the equation by subtracting 3400/139 from both sides:

2x = -18 - 3400/139

4. Simplify the right side of the equation:

2x = (-18 * 139 - 3400) / 139

5. Calculate the right side of the equation:

2x = (-2502 - 3400) / 139

2x = -5902 / 139

6. Divide both sides by 2 to isolate the variable x:

x = -5902 / (2 * 139)

x = -5902 / 278

x = -21.2115 (rounded to four decimal places)

Therefore, the solution to the equation 2x + 10(340/139) = -18 is x = -21.2115.

What value of x makes the equation true? 42/54= x/9 A. 2 B. 7 C. 14 D. 36

Answers

B) 7 would make it true, since both 42/54 and 7/9= 0.77 repeating

Cómo se puede describir a la regla o patrón de una sucesión .? *a)Expresión de números cortos.
b)Expresión algebraica.
c)Expresión multiple.

Answers

¡Hola! Creo que tu respuesta es una expresión algebraica B, aunque no estoy 100% seguro. ¡Espero que esto te ayude! Buena suerte y que tengas un gran día. ❤️

Alex played basketball 20 minutes longer on Tuesday than she did on Monday. She played for a total of 110 minutes for both days. Which equation can be used to find the number of minutes Alex played on Monday?