Question

Clara bought 16 cases of water bottles. There were 12 water bottles in each case. Four students wrote and solved equations to find b, the number of bottles that Clara bought. Which student wrote and solved the equation correctly? Maya's work: StartFraction b Over 12 EndFraction = 16. B = 1.3 Larissa's work: 12 b = 16. B = 1.3 Sally's work: StartFraction b Over 12 EndFraction = 16. B = 192. Anika's work: StartFraction 12 Over b EndFraction = 16. B = 192.

Answer 1

9514 1404 393

Answer:

  Sally's work: StartFraction b Over 12 EndFraction = 16. B = 192

Step-by-step explanation:

Of the offered choices, the only one that is solved correctly is Sally's work.

Here are the solutions for the equations the students wrote:

  $\dfrac{12}{b}=16\ \rightarrow\ 12=16b\ \rightarrow\ \dfrac{12}{16}=b=0.75\\\\\dfrac{b}{12}=16\ \rightarrow\ b=12\cdot16=192$

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Comment on the wrong answers

The "solution" value of 1.3 appears to be a rounded version of 16/12, a value that will not show up as a solution to any of the equations written.

Comment on dimensional analysis

The dimensions of "16" are "cases." The dimensions of "12" are "bottles per case", or bottles/case. Multiplying this by the number of cases, gives the number of bottles. This is where I'd start:

  (bottles/case)×(cases) = bottles    ⇒    12×16 = b

The ratios the students wrote had units of ...

  b/12 = (bottles)/(bottles/case) = cases = 16

and (incorrectly) ...

  12/b = (bottles/case)/(bottles) = 1/cases = 16 . . . . wrong

It can be useful to consider what the numbers represent. That can help avoid math mistakes.