1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
svlad2 [7]
3 years ago
14

Jimmy purchased 15 tickets to a concert and spent $140. He purchased some children's tickets and some adult tickets. The childre

n's tickets cost $7 each and the adult tickets cost $12 each. Write a system that represents this situation. How many of each did Jimmy purchase?​
Mathematics
1 answer:
fiasKO [112]3 years ago
4 0

Answer:

Jimmy purchased 8 of the children's ticket and 7 of the adult's ticket.

Step-by-step explanation:

Let c = children tickets

Let a = adult tickets

<u>Given the following data;</u>

Number of tickets = 15

Total amount spent = $140

Cost of each children ticket = $7

Cost of each adult ticket = $12

*Translating the word problem into an algebraic equation (system)*

<em>For the total number of tickets;</em>

c + a = 15 .........equation 1

<em>For the total amount spent;</em>

7c + 12a = 140 ..........equation 2

*Solving the linear equation by using the substitution method*

<em>Making c the subject in equation 1:</em>

c = 15 - a .......equation 3

<em>Substituting "c" into equation 2;</em>

7(15 - a) + 12a = 140

<em>Simplifying the equation, we have;</em>

105 - 7a +12a = 140

105 + 5a = 140

<em>Rearranging the equation, we have;</em>

5a = 140 - 105

5a = 35

a = \frac {35}{5}

a = 5 (For the $12 adult ticket).

To find the number of children tickets;

Substituting "a" into equation 3;

c = 15 - 7

c = 8 (For the $7 children ticket).

You might be interested in
A cicular pool with a radius of 12 meter if filled with water to a depth of 3 meters. what is the weight of water in the swimmin
Tcecarenko [31]
The weight of water in swimming pool is 13305600kg
5 0
3 years ago
. If α and β are the roots of
Lostsunrise [7]

Answer:

18x^2+85x+18 = 0

Step-by-step explanation:

<u><em>Given Equation is </em></u>

=> 2x^2+7x-9=0

Comparing it with ax^2+bx+c = 0, we get

=> a = 2, b = 7 and c = -9

So,

Sum of roots = α+β = -\frac{b}{a}

α+β = -7/2

Product of roots = αβ = c/a

αβ = -9/2

<em>Now, Finding the equation whose roots are:</em>

α/β ,β/α

Sum of Roots = \frac{\alpha }{\beta } + \frac{\beta }{\alpha }

Sum of Roots = \frac{\alpha^2+\beta^2  }{\alpha \beta }

Sum of Roots = \frac{(\alpha+\beta )^2-2\alpha\beta   }{\alpha\beta  }

Sum of roots = (\frac{-7}{2} )^2-2(\frac{-9}{2} ) / \frac{-9}{2}

Sum of roots = \frac{49}{4} + 9 /\frac{-9}{2}

Sum of Roots = \frac{49+36}{4} / \frac{-9}{2}

Sum of roots = \frac{85}{4} * \frac{2}{-9}

Sum of roots = S = -\frac{85}{18}

Product of Roots = \frac{\alpha }{\beta } \frac{\beta }{\alpha }

Product of Roots = P = 1

<u><em>The Quadratic Equation is:</em></u>

=> x^2-Sx+P = 0

=> x^2 - (-\frac{85}{18} )x+1 = 0

=> x^2 + \frac{85}{18}x + 1 = 0

=> 18x^2+85x+18 = 0

This is the required quadratic equation.

5 0
3 years ago
Read 2 more answers
Which expression has a value of 1/36?
Schach [20]
(1/36) = 0.0277777777778

(1/108)^3 = 7.9383224102<span> x 10^-7 </span>
(1/9)^4 = 0.000152415790276
(1/6)^2 = 0.0277777777778
(1/2)^5 =  <span>0.03125

The only one that matches with the value of 1/36 is (1/6)^2. Therefore, your answer is C. (1/6)^2
</span>




6 0
3 years ago
Read 2 more answers
alicia cashed her paycheck and used half of her earnings to take three friends to dinner. She spent $42.15 on dinner and she bro
Nana76 [90]
X - $42.15 > $20.00
<u>  + $42.15 + $42.15</u>
              x > $62.15
5 0
3 years ago
What is the slope of the line that passes through the points (6, -5) and (6, -8)?
Anni [7]
(6,-5) (6,-8)

y2-y1/x2-x1

-8+5/6-6

-3/0

Undefined should be the answer. Hope this helped (:
4 0
3 years ago
Other questions:
  • What is this mess. you will get 29 pts if you know
    15·2 answers
  • A line has slope 5/6 and y-intercept −3.
    9·2 answers
  • Can someone please help me find DC?
    9·2 answers
  • The height of a trapezoid is 13 yards. One of the bases is 2.5 times theheight, and the other base is two times the height. Find
    15·1 answer
  • what is an equation of the line that passes through the point(-5,-5) and is parallel to the line 3x-5y=25​
    12·1 answer
  • If p(x,y) is the point on the unit circle defined by real number theta, then tan theta= _____.
    14·2 answers
  • Simply 9+3(8-3(7-5))-4
    6·1 answer
  • Each of the figures below is made up of six squares three of the figures can be folded on the lines to form a cube which figure
    13·1 answer
  • Plllllzzzzzzzzz hurry
    7·2 answers
  • Which of the value is y?<br> y-32=21<br> y=47<br> y=53
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!