Back to Rearrange formulas — Problem 3 · Task Set 29

HSA.CED.A.4 Tutor Intake — Rearranging Formulas

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Grade 9·8 problems·~12 min·Common Core Math - HS Algebra·standard·hsa-ced-a-4

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Procedures

The total amount with simple interest is $A = P + Prt$ , where $A$ is
total amount, $P$ is principal, $r$ is rate, and $t$ is time.

To solve for $P$ , a student writes:

"Divide both sides by $rt$ : $\frac{A}{rt} = 1 + P$ , so $P = \frac{A}{rt} - 1$ ."

What error did the student make?

The student correctly isolated $P$ . The answer $P = \frac{A}{rt} - 1$
is right.

The student divided only the $Prt$ term by $rt$ , not the $P$ term.
The correct first step is to factor: $A = P(1 + rt)$ , then divide
by $(1 + rt)$ .

The student should have subtracted $Prt$ from both sides first.

The student should have multiplied both sides by $rt$ instead of
dividing.