Question

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.

Answer 1

Answer: B) a + c = 10

8a + 5c = 59

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 2

`\boxed{\boxed{\pink{\bf \leadsto Option \ second \ is \ correct .}}}`

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 :-

`\implies \bf No. \ of \ adult \ be \ denoted \ by \ a. \\\\\bf \implies No . \ of \ Children \ be \ denoted \ by \ c .`

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

`\implies \bf n_(adult) + n_(children) = 10 \\\\\bf\implies \boxed{\bf a + c = 10 }`

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

`\bf\implies n_(adult)* cost_(adult) + n_(child)* cost_(child) = Total \ cost \\\\\bf \implies a * \$ 8 + c * \$ 5 = \$ 59 \\\\\bf\implies \boxed{\bf 8a + 5c =\$ 59 }`

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

`\red{\bf Option \ 2 } \begin{cases} \bf a + c = 10 \\\\\bf 8a + 5c = 59 \end{cases}`

Hence second option is correct .