Question

Darren 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. Darren starts with 12 points, and his little brother starts with 30 points. Darren gets 3 points for every successful shot, and his brother, since he is younger, gets 1 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? Darren and his brother will have each made ______ shots, for a tied score of ______.

Answer 1

Darren and his brother will each have made 9 additional shots, for a tied score of 39 points.

Step-by-step explanation:

In order for Darren and his little brother to have a tied score in the game, they need to have an equal number of points. We can set up an equation to represent this:

12 + 3x = 30 + 1x

Where x represents the additional shots they each make. To solve for x, we can subtract 1x from both sides and subtract 12 from both sides:

2x = 18

Dividing both sides by 2 gives us:

x = 9

So, each brother will have made 9 additional shots. To find out the total points, we can substitute x = 9 into the equation:

Total points = 12 + 3(9) = 12 + 27 = 39

Therefore, Darren and his brother will have each made 9 shots, for a tied score of 39.