1. Mark is six years older than his brother Sam. The sum of their ages is 30. What a be Sam's age. Set up and solve an equation using the information given to find the value of a. 2. Alonso and Mandy are selling raffle tickets at a school for a fundraiser. Alonso sells five tickets lesson three times what Mandy sells. Together they saw a total of 43 tickets. What N equals the number of tickets Mandy sells. Use an equation to determine the number of tickets Alonso sells. Show how you arrived at your answer. 3. Elena, Karla, and Faye are playing a card game where they score points. Karla scores twice the number of points Elena does, and Faye scored 30 points more than Elena does. The sum of their three scores is 114. Who scores more points, Carla or Faye? Show how you found your answer. (Hint: what an equal the number of points Elena that scores.)

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.

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11 -1> 1 -1+ a

-12 > a