In a basketball game, a regular basket was worth 2 points and a long-distance basket was worth 3 points. If there were 45 baskets in a game and 96 points total, how many regular baskets r and long-distance baskets l were made? Show the correct system of equations.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that the number of regular baskets made is represented by 'r' and the number of long-distance baskets made is represented by 'l'.
According to the given information, a regular basket is worth 2 points, so the total points from regular baskets would be 2r. Similarly, a long-distance basket is worth 3 points, so the total points from long-distance baskets would be 3l.
The problem states that there were 45 baskets in total, so the sum of regular and long-distance baskets should be equal to 45. This can be expressed mathematically as:
r + l = 45 -- Equation 1
Also, the total points scored from all the baskets is given as 96. So, the sum of the points from regular and long-distance baskets should be equal to 96. This can be expressed mathematically as:
2r + 3l = 96 -- Equation 2
Thus, the correct system of equations for this problem is:
r + l = 45
2r + 3l = 96
You can solve this system of equations using various methods, such as substitution or elimination, to find the values of 'r' and 'l'.
Let's assume that the number of regular baskets made is represented by the variable "r," and the number of long-distance baskets made is represented by the variable "l."
The given information can be represented by the following equations:
1. The total number of baskets made: r + l = 45
2. The total number of points: 2r + 3l = 96
Therefore, the correct system of equations is:
r + l = 45
2r + 3l = 96
number of 2 point baskets --- x
number of 3 point baskets --- 45-x
2x + 3(45-x) = 96
2x + 135 - 3x = 96
-x = -39
x = 39
39 2pointers, and 6 3pointers
check:
39(2) + 6(3) = 96
39+6 = 45
Yeahh