100 POINTS!!A matinee ticket costs $6 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who saw a movie was 35, and the total money collected was $70. Which of the following options represents the number of children and the number of adults who saw a movie that day, and the pair of equations that can be solved to find the numbers? (4 points) 7 children and 28 adults Equation 1: a + c = 35 Equation 2: 6a − c = 70 7 children and 28 adults Equation 1: a + c = 35 Equation 2: 6a + c = 70 28 children and 7 adults Equation 1: a + c = 35 Equation 2: 6a + c = 70 28 children and 7 adults Equation 1: a + c = 35 Equation 2: 6a − c = 70
Accepted Solution
A:
We know: The total number of tickets is 35. Another way of saying this is the number of adults plus the number of children equals 35. i.e.:
[tex]Adults+Children=35[/tex]
Using the symbols provided we can write this is as:
[tex]a+c=35[/tex]
We also know: The total money collected is $75. We know that $6 was collected for every adult or [tex]6a[/tex] and $1 for every child or [tex]1c[/tex]. i.e.:
[tex](SixDollars \times Adults)+(OneDollar \ times Children)= $70[/tex]
Using the symbols provided and adding it all up we can write this is as: