16Hit1600
AlgebraHardSolving a linear model for the input

Algebra practice question

The balance of a loan, in dollars, after m monthly payments is modelled by B(m) = 150 − 12m. After how many payments will the balance be $30?

Answer: 10

Set B(m) = 30: 150 − 12m = 30. Subtract 150: −12m = −120. Divide by −12: m = 10. Check: 150 − 120 = 30.

Common wrong answers

If you answered 15
15 is (150 + 30) / 12, adding the 30 instead of subtracting it. The balance must FALL to 30, so 150 − 30 = 120 is what's paid off.
If you answered 120
120 is the amount paid off in dollars, not the number of payments. Divide by 12 per payment.
If you answered 12.5
12.5 is 150 / 12, the number of payments to reach ZERO. The question asks when the balance is 30, which comes sooner.

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