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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Wyatt and his little brother made up a game using coins. They flip the coins towards a cup and receive points for every one that makes it in. Wyatt starts with points, and his little brother starts with points. Wyatt gets points for every successful shot, and his brother, since he is younger, gets point for each successful shot. Eventually, the brothers will have a tied score in the game. How many additional shots will each brother have made? How many points will they both have?Wyatt and his brother will have each made ___ shots, for a tied score of ___.
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Wyatt and his little brother made up a game using coins. They flip the coins towards a cup and receive points for every one that makes it in. Wyatt starts with points, and his little brother starts with points. Wyatt gets points for every successful shot, and his brother, since he is younger, gets point for each successful shot. Eventually, the brothers will have a tied score in the game. How many additional shots will each brother have made? How many points will they both have?Wyatt and his brother will have each made ___ shots, for a tied score of ___.
- Define Variables: Let's define the variables:Let be the number of additional shots Wyatt makes.Let be the number of additional shots Wyatt's little brother makes.We know:Wyatt's initial points: Wyatt's points per shot: Wyatt's brother's initial points: Wyatt's brother's points per shot: We want to find out how many additional shots each brother will have made for a tied score.The system of equations to describe the situation is:For Wyatt: Total points = Initial points + (Points per shot Number of shots)For Wyatt's brother: Total points = Initial points + (Points per shot Number of shots)The equations are:Wyatt's points: Wyatt's brother's points: Since they will have a tied score, we can set the two expressions equal to each other:
- System of Equations: Now we need to solve the system using substitution. We can express in terms of from the first equation:Now we have an expression for that we can substitute back into the equation where the points are tied:
- Substitution: Simplify the equation:Now, we can subtract from both sides to see if we can solve for :Simplify the right side:This equation is true for all values of , which means we made a mistake. We should not have subtracted from both sides because it eliminates the variable we are trying to solve for. Let's go back and correct this mistake.
