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? a. r + l = 96; 2r + 3l = 45 66 regular; 30 long-distance b. r + l = 45; 2r + 3l = 96 39 regular; 6 long-distance c. r + l = 96; 3r + 2l = 45 33 regular; 12 long-distance d. r + l = 45; 3r + 2l = 96 37 regular; 8 long-distance

B. r + l = 45; 2r + 3l = 96

39 regular; 6 long-distance

Step-by-step explanation:

There were 45 baskets, so

(1) r + l = 45

There were 96 points in the game, so

(2) 2r + 3l = 96

Solve equation (1) for l

                    l = 45 – r     Substitute the value for l in Equation (2)

2r + 3(45 – r) = 96      Remove parentheses

 2r + 135 - 3r = 96      Combine like terms

         -r + 135 = 96      Subtract 135 from each side

                  -r = -39      Multiply each side by -1

                  r = 39      Substitute the value of r in Equation (1)

           39 + l = 45        Subtract 39 from each side

                   l = 6

Check:

(1) 39 + 6 = 45

         45 = 45

(2) 2×39 + 3×6 = 96

           78 + 18 = 96

                   96 = 96