// Numbas version: exam_results_page_options {"name": "Given a formula for something use it (drip rate)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "statement": "

Write the following question down on paper and evaluate it without using a calculator.

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If you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

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You are told that

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$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\text{volume (mL)} \\times \\text{drop factor (drops/mL)}}{\\text{time (hr)}\\times \\text{60 (min/hr)}}$

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If the volume is $\\var{v}$ mL, the duration is $\\var{h}$ hours and there are $\\var{f}$ drops/mL, then the drip rate is

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[[0]] (drops/min) to the nearest whole number

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We take the formula

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$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\text{volume (mL)} \\times \\text{drop factor (drops/mL)}}{\\text{time (hr)}\\times \\text{60 (min/hr)}}$

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and substitute the following

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$\\text{volume}=\\var{v}$,

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$\\text{drop factor}= \\var{f}$,

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$\\text{time}= \\var{h}$

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so that we have

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$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v} \\times \\var{f}}{\\var{h}\\times 60}$

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Using a calculator we would find

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\\begin{align}\\text{drip rate (dpm)}&\\approx\\var{drip} \\text{ dpm}\\\\&=\\var{driprounded}\\text{ dpm (to the nearest whole number)}\\end{align}

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Without a calculator, you could do this calculation by

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• first determining $\\var{v} \\times \\var{f}=\\var{vf}$,
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• then $\\var{h} \\times 60=\\var{hs}$,
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• and then using long division for  $\\displaystyle \\frac{\\var{vf}}{\\var{hs}} =\\var{driprounded}$ (nearest whole number).
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However, it is often best to look for common factors and cancel them before the multiplication and division. That is, given:

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$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v} \\times \\var{f}}{\\var{h}\\times 60}$

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I would look for a common factor between $\\var{v}$ and $\\var{h}$.  But, alas, there isn't one. There is a common factor of $\\var{cfvh}$, so I'd remove this from the top and bottom and be left with

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$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v'} \\times \\var{f}}{\\var{h'}\\times 60}$

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Then I'd look for a common factor between $\\var{v'}$ and $\\var{60}$. But, alas, there isn't one. There is a common factor of $\\var{cfvs}$, so I'd remove that from the top and bottom and be left with

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$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v''} \\times \\var{f}}{\\var{h'}\\times \\var{s'}}$

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Then I'd look for a common factor between $\\var{f}$ and $\\var{h'}$. But, alas, there isn't one. There is a common factor of $\\var{cffh'}$, so I'd remove that from the top and bottom and be left with

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$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v''} \\times \\var{f'}}{\\var{h''}\\times \\var{s'}}$

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Then I'd look for a common factor between $\\var{f'}$ and $\\var{s'}$. But, alas, there isn't one. There is a common factor of $\\var{cffs'}$, so I'd remove that from the top and the bottom and be left with

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$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v''} \\times \\var{f''}}{\\var{h''}\\times \\var{s''}}$

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So, after all that, I only need to do

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• $\\var{v''} \\times \\var{f''}=\\var{vf''}$,
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• then $\\var{h''} \\times \\var{s''}=\\var{hs''}$,
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• and then perform the division $\\displaystyle \\frac{\\var{v''*f''}}{\\var{s''*h''}}=\\var{driprounded}$ (nearest whole number)
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