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Verizon [17]
2 years ago
8

Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost $228. Write and solve a s

ystem of equations to find how many children and how many adults were in the group. (Define variables, write equations, solve, write a sentence)
Mathematics
1 answer:
kifflom [539]2 years ago
6 0

Answer:

Adults= 7

children= 9

Step-by-step explanation:

Step one:

given data

Adult tickets to a play cost $22. Tickets for children cost $15

let adult be x

and children be y

so

22x+15y= 228------1

x+y= 11----------------2

x= 11-y

Step two:

from 1

22(11-y)+15y= 228

242-22y+15y= 228

collect like terms

-7y= 228-242

7y= 14

divide both sides by 7

x= 2

from

x+y=11

y=11-2

y= 9

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\huge\textbf{Hey there!}

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\rightarrow\mathbf{7 \dfrac{1}{6} = 5\dfrac{2}{5} + p}

\mathbf{\rightarrow p + 5\dfrac{2}{5}= 7\dfrac{1}{6}}

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\text{SUBTRACT }\rm{\dfrac{27}{5}}\text{ to BOTH SIDES}

\mathbf{p + \dfrac{27}{5} - \dfrac{27}{5} = \dfrac{43}{6}- \dfrac{27}{5}}

\text{CANCEL out: }\rm{\dfrac{27}{5} - \dfrac{27}{5}}\text{ because it gives you 0}

\text{KEEP: }\rm{\dfrac{43}{6} - \dfrac{27}{5}}\text{ because it help solve for the p-value}

\text{NEW EQUATION: }\rm{p = \dfrac{43}{6} - \dfrac{27}{5}}

\large\textsf{SIMPLIFY IT!}

\mathbf{p = \dfrac{53}{30} \approx p = 1\dfrac{23}{30}}

\huge\boxed{\textsf{Therefore, your answer is: \boxed{\mathsf{p = 1\dfrac{23}{30}}}}}\huge\checkmark

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Please answerrrrr<br><br> Thank you!!!!!!!!!!!!
dlinn [17]

The correct answers are:

_________________

 " (x − 13) ° = 53 ° " ;

_________________

 " x = 66 " ;

_________________

 " m∠2 = 55° " ;

_________________

 " m∠1 = 55° " .

__________________

<u>Step-by-step explanation</u>:

Note:  The following "given values/answers" within the attached image:

Specifically:

 (x − 13)° = 72° ; and;

  x = 85° ;

_________________

   are: "incorrect"—and are "arbitrarily assigned values"

_________________

The values and expressions given in the attached image, however, are correct/do make sense; and we can use such data to solve the problem.

_________________

Let's start by finding the measure of ∠2 ;  that is: " m∠2 " :

To find m∠2:

_________________

Note that:  both: "∠2 " ; and the angle that measures "175" with the attached image:

            → both form a <u>straight line</u>—that is;

              → they are "supplementary angles" ;

              → which means they add up to "180° " ;

_________________

So:  To solve for:  "m∠2" :

_________________

→  m∠2 = 180 − (125) = 55° ,

_________________

Now; to solve for:  " m∠1 " :

_________________

Note that ∠1 and ∠2 are vertical angles: which means that they have equal measurements;  

{since: vertical angles are congruent; which means that vertical angles are equal.} ;

_________________

→  As such, m∠1 = m∠2 = 55 °.

_________________

Now, take either ∠1 or ∠2 ; (each has the same "measurement"—"55° " ;

 And combine with angle with the given measurement of 72° ;

 And combine with the angle with the "given measurement of [the expression: ["x − 13"]° ;

_________________

All three of these angles form a <u>straight line</u>—that is;

              → they are "supplementary angles" ;

              → which means they add up to "180° " ;

So, 55° + 72° + (x − 13)° = 180° ;

 Let us solve for "x" ; and for "(x − 13)" ;

_________________

55 + 72 = 127 ;

→ 127 + (x − 13) = 180 ;

Now, subtract "127" from each side of the equation:

_________________

 → 127 + (x − 13) − 127 = 180 − 127 ;

   to get:

          " (x − 13) = 53 " ; →  which is one of our answers;

 Now, to solve for "x" ; we add "13" to Each Side of the equation;

   to isolate "x" on one side of the equation; & to solve for "x" :

_________________

      x − 13 + 13 = 53 + 13 ;

to get:

_________________

      x  = 66 ;

_________________

So:  The correct answers are:

_________________

 " (x − 13) ° = 53 ° " ;

  → Double check by substituting our value of "66" for "x" :

 " (66 − 13) =? 53 ?  Yes!  ;

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 " x = 66 " ;

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 " m∠2 = 55° " ;

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 " m∠1 = 55° " .

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Hope these answers—and explanations—are helpful!

  Best wishes!

_________________

3 0
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