Hot Shot is an arcade basketball game in which the object is to make as many baskets as possible within the 60-second time limit. A player is awarded 2 points for each successful shot during the first 50 seconds of play and 3 points per successful shot during the final 10 seconds.
Tyler had a bit of beginner’s luck in her first game scoring a total of 60 points. She wants to exceed this total in her second game. What is the minimum number of baskets Tyler must make to earn a score greater than 60 points?
To find the minimum number of baskets Tyler must make to earn a score greater than 60 points, we need to determine how many shots she can make in each time period (first 50 seconds and final 10 seconds) and calculate the total score for each scenario.
First, let's consider how many shots Tyler could make during the first 50 seconds. Each successful shot is worth 2 points, so the total score for this period can be calculated as:
Score during first 50 seconds = 2 points * Number of successful shots during first 50 seconds
Next, let's consider how many shots Tyler could make during the final 10 seconds. Each successful shot is worth 3 points, so the total score for this period can be calculated as:
Score during final 10 seconds = 3 points * Number of successful shots during final 10 seconds
Since Tyler wants to exceed her first game's score of 60 points, we can set up an inequality:
Score during first 50 seconds + Score during final 10 seconds > 60
Let's find the minimum number of baskets for Tyler by considering two scenarios:
Scenario 1: Tyler does not make any shots during the final 10 seconds.
In this case, the maximum score Tyler can achieve is:
Score during first 50 seconds = 2 points * Number of successful shots during first 50 seconds
To exceed a score of 60 points, we need:
2 points * Number of successful shots during first 50 seconds > 60
Solving this inequality, we get:
Number of successful shots during first 50 seconds > 30
So, Tyler must make more than 30 baskets during the first 50 seconds to exceed a score of 60 points.
Scenario 2: Tyler makes at least one shot during the final 10 seconds.
In this case, the maximum score Tyler can achieve is:
Score during first 50 seconds + Score during final 10 seconds = 2 points * Number of successful shots during first 50 seconds + 3 points * Number of successful shots during final 10 seconds
To exceed a score of 60 points, we need:
2 points * Number of successful shots during first 50 seconds + 3 points * Number of successful shots during final 10 seconds > 60
Solving this inequality depends on the specific number of successful shots during the final 10 seconds.
By considering both scenarios and evaluating the minimum number of baskets Tyler must make, we can conclude that Tyler needs to make more than 30 baskets during the first 50 seconds in order to exceed a score of 60 points.