Solved Examples: The Customary System of Measurements and Units

Samuel Dominic Chukwuemeka (SamDom For Peace)

For ACT Students
The ACT is a timed exam...60 questions for 60 minutes
This implies that you have to solve each question in one minute.
Some questions will typically take less than a minute a solve.
Some questions will typically take more than a minute to solve.
The goal is to maximize your time. You use the time saved on those questions you solved in less than a minute, to solve the questions that will take more than a minute.
So, you should try to solve each question correctly and timely.
So, it is not just solving a question correctly, but solving it correctly on time.
Please ensure you attempt all ACT questions.
There is no negative penalty for any wrong answer.

For JAMB and CMAT Students
Calculators are not allowed. So, the questions are solved in a way that does not require a calculator.

Solve all questions.
Use at least two methods as applicable.
State the measurement.
Show all work.

NOTE: Unless specified otherwise:
(1.) Use only the tables provided for you.
(2.) Please do not approximate intermediate calculations.
(3.) Please do not approximate final calculations. Leave your final answer as is.

Customary to Customary Conversions
Quantity	Customary	Customary	Unit Conversion Factor
Length	inch (in)	foot (ft)	$12\:inches = 1\:ft$
Length	foot (ft)	yard (yd)	$3\:ft = 1\:yd$
Length	yard (yd)	mile (mi)	$1760\:yd = 1\:mi$
Length	foot (ft)	mile (mi)	$5280\:ft = 1\:mi$
Length	rod/pole	yards (yd)	$1\:rod = 5.5\:yd$
Length	furlong	rod	$1\:furlong = 40\;rod$
Length	fathom	feet (ft)	$1\:fathom = 6\;ft$
Length	league/marine	nautical miles	$1\:league = 3\;nautical\;\;miles$
Mass	pound (lb)	ounce (oz)	$1\:lb = 16\:oz$
Mass	short ton (ton)	pound (lb)	$1\:short\:ton = 2000\:lb$
Mass	long ton	pound (lb)	$1\:long\:ton = 2240\:lb$
Mass	stone	pound (lb)	$1\:\:stone = 14\:lb$
Mass	long ton	stone	$1\:long\:ton = 160\:stones$
Area	acre (acre)	square feet ($ft^2$)	$1\:acre = 43560\:ft^2$
Volume	quart (qt)	pint (pt)	$1\:qt = 2\:pt$
Volume	pint (pt)	cup (cup)	$1\:pt = 2\:cups$
Volume	quart (qt)	cup (cup)	$1\:qt = 4\:cups$
Volume	quart (qt)	fluid ounce (fl. oz)	$1\:qt = 32\:fl.\:oz$
Volume	pint (pt)	fluid ounce (fl. oz)	$1\:pt = 16\:fl.\:oz$
Volume	cup (cup)	fluid ounce (fl. oz)	$1\:cup = 8\:fl.\:oz$
Volume	gallon (gal)	quart (qt)	$1\:gal = 4\:qt$
Volume	gallon (gal)	quart (pt)	$1\:gal = 8\:pt$
Volume	gallon (gal)	cup (cup)	$1\:gal = 16\:cups$
Volume	gallon (gal)	fluid ounce (fl. oz)	$1\:gal = 128\:fl.\:oz$
Volume	gallon (gal)	cubic inches ($in^3$)	$1\:gal = 231\:in^3$

(1.) Convert 26400 yards to miles

Measurement is Length

$ \underline{First\:\:Method:\:\:Unity\:\:Fraction\:\:Method} \\[3ex] 26400\:yd\:\:to\:\:mi \\[3ex] = 26400\:yd * \dfrac{.....mi}{.....yd} \\[5ex] = 26400\:yd * \dfrac{1\:mi}{1760\:yd} \\[5ex] = \dfrac{26400}{1760}\:mi \\[5ex] = 15\:mi \\[3ex] \underline{Second\:\:Method:\:\:Proportional\:\:Reasoning\:\:Method} \\[3ex] 1760\:yd = 1\:mi \\[3ex] Let\:\:p = length\:\:of\:\:26400\:yd\:\:in\:\:mi \\[3ex] $

$yard$	$mile$
$1760$	$1$
$26400$	$p$

$ \dfrac{p}{1} = \dfrac{26400}{1760} \\[5ex] p = 15\:mi \\[3ex] \therefore 26400\:yd = 15\:mi $

(2.) Convert 15 feet to inches.

Measurement is Length

$ \underline{First\:\:Method:\:\:Unity\:\:Fraction\:\:Method} \\[3ex] 15\:ft\:\:to\:\:in \\[3ex] = 15\:ft * \dfrac{.....in}{.....ft} \\[5ex] = 15\:ft * \dfrac{12\:in}{1\:ft} \\[5ex] = 180\:in \\[5ex] \underline{Second\:\:Method:\:\:Proportional\:\:Reasoning\:\:Method} \\[3ex] 12\:in = 1\:ft \\[3ex] Let\:\:p = length\:\:of\:\:15\:feet\:\:in\:\:inches \\[3ex] $

$inch$	$feet$
$12$	$1$
$p$	$15$

$ \dfrac{p}{12} = \dfrac{15}{1} \\[5ex] p * 1 = 12 * 15 \\[3ex] p = 300 \\[3ex] $ 15 feet = 180 inches

(3.) Convert $5\dfrac{3}{8}$ pounds to ounces

Measurement is Mass

$ \underline{First\:\:Method:\:\:Unity\:\:Fraction\:\:Method} \\[3ex] 5\dfrac{3}{8}\:lb\:\:to\:\:oz \\[5ex] 5\dfrac{3}{8} = \dfrac{8 * 5 + 3}{8} = \dfrac{40 + 3}{8} = \dfrac{43}{8} \\[5ex] \dfrac{43}{8}\:lb\:\:to\:\:oz \\[5ex] = \dfrac{43}{8}\:lb * \dfrac{.....oz}{.....lb} \\[5ex] = \dfrac{43}{8}\:lb * \dfrac{16\:oz}{1\:lb} \\[5ex] = 43(2)\:oz \\[5ex] = 86\:oz \\[3ex] \underline{Second\:\:Method:\:\:Proportional\:\:Reasoning\:\:Method} \\[3ex] 1\:lb = 16\:oz \\[3ex] Let\:\:p = mass\:\:of\:\:\dfrac{43}{8}\:lb\:\:in\:\:oz \\[3ex] $

$pound$	$ounce$
$1$	$16$
$\dfrac{43}{8}$	$p$

$ \dfrac{p}{16} = \dfrac{\dfrac{43}{8}}{1} \\[7ex] \dfrac{p}{16} = \dfrac{43}{8} \\[5ex] Multiply\:\:both\:\:sides\:\:by\:\:16 \\[3ex] 16 * \dfrac{p}{16} = 16 * \dfrac{43}{8} \\[5ex] p = 2(43)\:oz \\[3ex] p = 86\:oz \\[3ex] \therefore 5\dfrac{3}{8}\:lb = 86\:oz $

(4.) Convert 37 feet to yards.

Measurement is Length

$ \underline{First\:\:Method:\:\:Unity\:\:Fraction\:\:Method} \\[3ex] 37\:ft\:\:to\:\:yd \\[3ex] = 37\:ft * \dfrac{.....yd}{.....ft} \\[5ex] = 37\:ft * \dfrac{1\:yd}{3\:ft} \\[5ex] = 12.33333333\:yd \\[5ex] \underline{Second\:\:Method:\:\:Proportional\:\:Reasoning\:\:Method} \\[3ex] 3\:ft = 1\:yd \\[3ex] $

$feet$	$yard$
$3$	$1$
37	what

$ \dfrac{what}{1} = \dfrac{37}{3} \\[5ex] what = 12.33333333\:yd \\[3ex] $ 37 feet = 12.33333333 yards

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