HELP ASAP NEED THE ANSWER LIKE RIGHT NOW 100 POINTS AND WILL GIVE BRAINLIEST 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

a + c = 30

8a + c = 100

a=10, c= 20

Step-by-step explanation:

cost = 8a + 1c  since it is 8 dollars for adult and 1 for child where a is the number of adults and c is the number of children

a+c = 30  since we know that 30 adults and children went

100 = 8a + 1c   and it cost 100 dollars

Let c =30 -a

100 = 8a + (30-a)

100 = 7a +30

Subtract 30 from each side

70 = 7a

Divide by 7

10 =a

Then a+c = 30

10+c = 30

c = 30-10

c = 20

eqn1 : a +c=30

eqn2: 8a+c=100

20 children and 10 adults

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204