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A school fair ticket costs $8 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who went to the fair was 30, and the total money collected was $100. Which of the following options represents the number of children and the number of adults who attended the fair that day, and the pair of equations that can be solved to find the numbers?
20 children and 10 adults
Equation 1: a + c = 30
Equation 2: 8a + c = 100
10 children and 20 adults
Equation 1: a + c = 30
Equation 2: 8a − c = 100
10 children and 20 adults
Equation 1: a + c = 30
Equation 2: 8a + c = 100
20 children and 10 adults
Equation 1: a + c = 30
Equation 2: 8a − c = 100

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Seprum
The correct system of equations is:
[tex] \left \{ {{a+c=30} \atop {8a+c=100}} \right. [/tex]

Let's express [tex]a[/tex] from first equation:
[tex]a=30-c[/tex]

Now let's replace [tex]a[/tex] in second equation with found expression and solve it:
[tex]8(30-c)+c=100[/tex]
[tex]240-8c+c=100[/tex]
[tex]7c=240-100[/tex]
[tex]7c=140[/tex]
[tex]c=140/7=20[/tex]

Finally, let's replace [tex]c[/tex] with found value in first equation and solve it too:
[tex]a+20=30[/tex]
[tex]a=30-20=10[/tex]

So, the correct answer is:
20 children adn 10 adults
Equation 1: a + c = 30
Equation 2: 8a + c = 100
The answer will be Equation 1: a + c = 30
Equation 2: 8a + c = 100, where 20 children and 10 adults. Hope it help!

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