Question

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

Answer 1

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

39 regular; 6 long-distance

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

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Check:

(1) 39 + 6 = 45

45 = 45

(2) 2×39 + 3×6 = 96

78 + 18 = 96

96 = 96