Answer:
129 points
Step-by-step explanation:
Let L and C represent the scores of Luke and Caleb, respectively.
L = 2C -15 . . . . . Luke scored 15 less than twice the number Caleb did
L +C = 201 . . . . . they scored 201 points altogether
Add twice the second equation to the first:
2(L +C) + (L) = 2(201) + (2C -15)
3L +2C = 387 +2C . . . . simplify
3L = 387 . . . . . . . . . . . . .subtract 2C
L = 387/3 = 129 . . . . . . .divide by 3
Luke scored 129 points.
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<em>Comment on the solution</em>
Normally, you might solve this set of equations by substitution, since you have an expression for L in terms of C. Doing that would give a value for C, and an extra step would be required to find L. We wanted to avoid the step of finding C, since that was not a value we needed to know.
You could also substitute 201-L for C, which is effectively what we did. After substitution, that equation looks like ...
L = 2(201-L) -15
L = -2L +387 . . . . simplify
Adding 2L and dividing by 3 gets the same result as above.
