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Write a system of equations for the following situation:
A group of 10 people went to see a movie. The cost to go to the movie is $8 for an adult and $5 for a child. The total cost for the group was $59.

Write A System Of Equations For The Following Situation A Group Of 10 People Went To See A Movie The Cost To Go To The Movie Is 8 For An Adult And 5 For A Child class=

Sagot :

Answer: B) a + c = 10

8a + 5c = 59

Step-by-step explanation:

We know that 10 total people went, so the first equation has to be equal to 10. The total was $59, so the second equation should be set equal to $59. Now that the second equation is for cost, we must make it 8a + 5c to represent the cost of the adult and child tickets which are $8 and $5, respectively.

Answer:

[tex]\boxed{\boxed{\pink{\bf \leadsto Option \ second \ is \ correct .}}}[/tex]

Step-by-step explanation:

Given that , a group of 10 people went to see a movie. The cost to go to the movie is $8 for an adult and $5 for a child. The total cost for thegroup was $59.

Let :-

[tex]\implies \bf No. \ of \ adult \ be \ denoted \ by \ a. \\\\\bf \implies No . \ of \ Children \ be \ denoted \ by \ c . [/tex]

Since the total number of people in group is 10 . Then ,

[tex]\implies \bf n_{adult} + n_{children} = 10 \\\\\bf\implies \boxed{\bf a + c = 10 }[/tex]

Now , the cost for an adult is $8 and for a child is $5. Hence ,

[tex]\bf\implies n_{adult}\times cost_{adult} + n_{child}\times cost_{child} = Total \ cost \\\\\bf \implies a \times \$ 8 + c \times \$ 5 = \$ 59 \\\\\bf\implies \boxed{\bf 8a + 5c =\$ 59 }[/tex]

Hence our overall answer matches with second option .That is ,

[tex]\red{\bf Option \ 2 } \begin{cases} \bf a + c = 10 \\\\\bf 8a + 5c = 59 \end{cases}[/tex]

Hence second option is correct .

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