Question

Jayden and his cousin are playing a game where they pick up colored sticks. Jayden currently has 20 points and likes to pick up the green sticks, earning 7 points every turn. His cousin just lost all her points on the previous turn, and has a strategy to catch up by getting all the red ones, earning 9 points per turn. In a certain number of turns, the score will be tied. How many points will they each have?

Answer 1

After 10 turns, Jayden and his cousin will each have 90 points, thus, the scores will be tied.

Step-by-step explanation:

Jayden and his cousin are playing a game where they pick up colored sticks. Jayden, who already has 20 points, earns 7 points every turn by picking up green sticks. His cousin, starting from zero points after losing all her points, earns 9 points per turn by picking up red sticks. To find out after how many turns the scores will be tied, we can set up an equation:

Let t be the number of turns. Jayden's points after t turns will be 20 + 7t, and his cousin's points will be 9t. To have the scores tied, we need:

20 + 7t = 9t

Subtract 7t from both sides to get:

20 = 2t

Now divide both sides by 2 to find the number of turns:

t = 10

After 10 turns, Jayden's score will be 20 + (7 * 10) = 90 points, and his cousin's score will be 9 * 10 = 90 points, so they will be tied at 90 points each.