Question

Matt and Seth purchase baseball cards each week. the amount of cards they each have in their collection is shown in the graph and table. who will have more cards in week 20?

Answer 1

Seth will have more cards in 20 weeks. The reason for this is because Seth gains 4 more cards a week while Matt only gains 2 More cards a week. So in 20 weeks Seth will have 80 Baseball cards while Matt has 40 Cards.

Explanation:

Answer 2

At the end of Week 20;

Seth has 58 balls

Matt has 20 balls

Seth has more balls

Explanation:

The graph shows a progression

Week 1:

Matt has 1, Seth has 22

Week 5:

Matt has 5, Seth has 30:

Week 9:

Matt has 9, Seth has 38

For Matt, the progression shows that;

Matt bought (5 - 1) baseball's between week 1 and 5 and (9 - 5) between week 9 and 5

(5 - 1) balls = (9 - 5) balls

=> 4 balls = 4 balls

(9 - 5) weeks = (5-1) weeks

4 weeks = 4 weeks

4 weeks = 4 balls. --- divide by 4

1 weeks = 1 ball

This means that Matt buys a ball per week; Common difference = 1

For Matt, the progression shows that;

Matt bought (30 - 22) baseball's between week 1 and 5 and (38 - 30) between week 9 and 5

(30 - 22) balls = (38 - 30) balls

=> 8 balls = 8 balls

(9 - 5) weeks = (5-1) weeks

4 weeks = 4 weeks

4 weeks = 8 balls. --- divide by 4

1 seek = 2 ball

This means that Sett buys 2 balls ball per week --- Common difference = 2

Calculating their balls at week 20;

Using the following formula

Tn = a + (n-1)d.

Where a = first term

n = nth term

d = common difference

For Matt

a = 1

d = 1

n = 20

Tn = a + (n-1)d becomes

T20 = 1 + (20 - 1) * 1

T20 = 1 + 19 * 1

T20 = 20

For Seth

a = 22

d = 2

n = 20

Tn = a + (n-1)d becomes

T20 = 22 + (20 - 1) * 2

T20 = 22 + 19 * 2

T20 = 22 + 38

T20 = 58.

At the end of Week 20;

Seth has 58 balls

Matt has 20 balls

Seth has more balls