Question

Someone please help me with this question

Tony and his cousin are playing a game where they pick up colored sticks. Tony currently has 12 points and likes to pick up the yellow sticks, earning 10 points every turn. His cousin just lost all his points on the previous turn, and has a strategy to catch up by getting all the blue ones, earning 14 points per turn. In a certain number of turns, the score will be tied. How many points will they each have? How long will that take?

Tony and his cousin will each have __ points in __ turns.

Answer 1

• 42 points
• 3 turns

Explanation:

You want to know the number of points and the number of turns when Tony and his cousin will have the same score. Tony has 12 points and earns 10 points per turn; his cousin has 0 points and earns 14 points per turn.

Table

The attachment shows a table of points and turns. It shows the score will be tied at 42 points after 3 turns.

Equations

Tony's points can be described by ...

p = 12 +10t . . . . . . . . 12 points in addition to 10 per turn

Cousin's points can be described by ...

p = 0 + 14t . . . . . . . . . 14 points per turn added to the current score of 0

These will be equal when ...

p = p

12 +10t = 0 +14t . . . . substitute for p in both cases

12 = 4t . . . . . . . . . . subtract 10t

3 = t . . . . . . . . . . divide by 4

p = 14·3 = 42 . . . . the scores after 3 turns