Answer:
1) Sam's age = a = 12
Mark's age = 18
2) Number of tickets Mandy sells = N = 12
Number of tickets Alonso sells = 31
3) Number of points Elena scores = a = 12
Number of points Karla scores = 24
Number of points Faye scores = 42
Faye scores more points!
Step-by-step explanation:
1) Let a represent Sam's age
Mark's age = a + 6
Sum of their ages = 30
a + (a + 6) = 30
2a + 6 = 30
2a = 24
a = 12 year old
a + 6 = 12 + 6 = 18 year old
Sam's age = 12
Mark's age = 18
2) Let N represent the number of tickets that Mandy sells
Alonso sells five tickets less than three times Mandy sells, that is equal to (3N - 5) tickets.
Total number of tickets sold = 43
N + 3N - 5 = 43
4N = 48
N = 12 tickets
3N - 5 = 36 - 5 = 31 tickets
Number of tickets Mandy sells = N = 12
Number of tickets Alonso sells = 31
3) Let the number of points Elena scores = a
Number of points Karla scores = 2a
Number of points Faye scores = a + 30
Total number of points = 114
a + 2a + a + 30 = 114
4a = 114 - 30 = 84
4a = 84
a = 12 points
2a = 24 points
a + 30 = 42 points
Number of points Elena scores = a = 12
Number of points Karla scores = 24
Number of points Faye scores = 42
Since 42>24, Faye evidently scores more points than Carla.
