Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Nick and his cousin are playing a game where they pick up colored sticks. Nick currently has 14 points and likes to pick up the green sticks, earning 9 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 pink ones, earning 10 points per turn. In a certain number of turns, the score will be tied. How long will that take? How many points will they each have? In _____ turns, both players will have _____ points.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Nick and his cousin are playing a game where they pick up colored sticks. Nick currently has 14 points and likes to pick up the green sticks, earning 9 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 pink ones, earning 10 points per turn. In a certain number of turns, the score will be tied. How long will that take? How many points will they each have?   In _____ turns, both players will have _____ points.

Bytelearn · Accepted Answer

Define variables: Let's define the variables for the number of turns it will take for Nick and his cousin to tie and the points they will each have. Let x represent the number of turns, and let P represent the points they will each have at the tie.Calculate Nick's points: Nick starts with 14 points and earns 9 points every turn. So, after x turns, Nick will have 14 + 9x points.Calculate cousin's points: His cousin starts with 0 points and earns 10 points every turn. So, after x turns, his cousin will have 0 + 10x points.Set up equation: For their scores to be tied, the points Nick has must be equal to the points his cousin has. This gives us the equation: 14 + 9x = 10xSolve equation: To find the value of x, we need to solve the equation. We can do this by isolating x on one side of the equation: 14 + 9x = 10x 10x - 9x = 14 x = 14Find cousin's points: Now that we have the number of turns (x), we can find out how many points they will each have. Since Nick's cousin earns 10 points per turn, after 14 turns, she will have: 10 * 14 = 140 pointsCheck Nick's points: We can check if Nick will also have 140 points after 14 turns: 14 + 9 * 14 = 14 + 126 = 140 pointsFinal result: Therefore, in 14 turns, both players will have 140 points.

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