16Hit1600
AlgebraVery hardFind parameter giving infinitely many solutions

Algebra practice question

A video game studio is tuning two weapons so that they deal identical damage at every player level L. Weapon A deals (3/8)(16L - 24) + cL + 7 points of damage, and Weapon B deals 2(6L - 1) - L points of damage, where c is a constant.

If the two expressions give the same damage for every value of L, what is the value of c?

Answer: 5

Weapon A simplifies to 6L - 9 + cL + 7 = (6 + c)L - 2. Weapon B simplifies to 12L - 2 - L = 11L - 2. For the equation (6 + c)L - 2 = 11L - 2 to hold for every value of L, the coefficients of L must be equal: 6 + c = 11, so c = 5. (The constant terms are already equal, -2 = -2, which is what makes infinitely many solutions possible.)

Common wrong answers

If you answered 6
You dropped the -L at the end of Weapon B: 2(6L - 1) - L is 11L - 2, not 12L - 2, so 6 + c = 11 and c = 5.
If you answered 11
That's the coefficient of L in Weapon B's simplified form, but Weapon A already contributes 6L on its own, so c must make 6 + c = 11.
If you answered -5
You reversed the subtraction: 6 + c = 11 gives c = 11 - 6 = 5, not 6 - 11.

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