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timurjin [86]
3 years ago
9

Tickets to a local circus cost $5 for students and $8 for adults. A group of 9 people spent a total of $60. How many adults were

in the group?
Mathematics
1 answer:
S_A_V [24]3 years ago
3 0

Answer:

5

Step-by-step explanation:

You need to set up and solve a system of linear equations here.

Let s and a represent the number of students and adults respectively.

Then s + a = 9, and s = 9 - a.

Total ticket cost for the adults was ($8/adult)(a)

and for the students ($5/student)(s).

Total cost of the tickets was then  ($8/adult)(a) + ($5/student)(s) = $60.

Then our system of linear equations is:

8a + 5s = 60

 a  +  s  = 9, or s = 9 - a.  Substituting 9 - a for s, we get:

8a + 5(9 - a) = 60.

Then 8a + 45 - 5a = 60, or 3a = 15.

Solving for a, we get a = 5.

Solving for s using s = 9 - a, we get   s = 9 - 5, or s = 4.

There were 5 adults in the group (and 4 students).

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Given that 4x-5y = 21 Find x when y = -4. Give your answer as a fraction in its simplest form.
alexira [117]

Answer:

x = 1/4

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
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Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

4x - 5y = 21

<em>y</em> = -4

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Substitute in <em>y</em>:                                                                                                  4x - 5(-4) = 21
  2. Multiply:                                                                                                             4x + 20 = 21
  3. [Subtraction Property of Equality] Subtract 20 on both sides:                      4x = 1
  4. [Division Property of Equality] Divide 4 on both sides:                                  x = 1/4
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Answer:

Step-by-step explanation:

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y1 = (x + 2)(x - 5)

Notice that the x changes sigh. You say that the zeros are -2 and  5. To get y1 to go to zero, you must make x the opposite sign of what you are given.

Now you have to expand the factored form to get the standard form

y = x^2 + 2x - 5x - 10

y = x^2 - 3x - 10

That's not the right answer.

f(0) = 30 but you have - 10 at the end so you have to multiply the factored form by - 3

-3(f(x)) = -3(x + 2)(x - 5)

-3(f(x)) = -3(x^2 - 3x - 10)

f(x) = -3x^2 + 9x + 30    

f(0) = -3(0)^2 + 9(0) + 30

f(0) = 30

The quadratic still has roots of (x +2)(x - 5) but that 3 makes the y intercept = 30.

See the graph below.

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Step-by-step explanation:

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