Scales 3

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Scales 3

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Question 1 of 3

A map indicates that the distance between a town to the beach is

65 cm

$65 \text(cm)$ . If the scale of the map is

1 : 50 000

$1:50 000$ , what is the actual distance between the town and the beach in kilometres?

(32.5) $km$ $\text(km)$

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A scale is the ratio of the size of a model to the actual object it represents.

Quad boxes are used to easily find rates

First, fill up the quad boxes with the three known values and have the unknown value be

x

$x$ .

Map	Land
$1$ $1$	$50 000$ $50 000$
$65$ $65$	$x$ $x$

Next, equate the two columns and solve for

x

$x$ .

$\frac{1}{65}$ $1/(65)$	$=$ $=$	$\frac{50 000}{x}$ $(50 000)/x$

$1 (x)$ $1(x)$	$=$ $=$	$50 000 (65)$ $50 000(65)$	Cross multiply
$x$ $x$	$=$ $=$	$3 250 000$ $3 250 000$

Since the given measurement for the map is in

cm

$\text(cm)$ , this value will be

3 250 000 cm

$3 250 000 \text(cm)$ .

Finally, convert the centimetres into kilometres.

1 kilometre

$1 \text(kilometre)$

=

$=$

100 000 centimetres

$100 000 \text(centimetres)$

$x$ $x$	$=$ $=$	$3 250 000 \times \frac{1}{100 000}$ $3 250 000xx1/(100 000)$	$100 000 c m$ $100 000cm$ has $5$ $5$ zeroes $∴$ $:.$ move $5$ $5$ decimal places to left

$x$ $x$	$=$ $=$	$\frac{3 250 000}{100 000}$ $(3 250 000)/(100 000)$

	$=$ $=$	$32.5$ $32.5$

x = 32.5 km

$x=32.5 \text(km)$

Question 2 of 3

2. Question
A model plane has a wingspan of $61 cm$ $61 \text(cm)$ . What would the actual wingspan be in metres if the scale is $1 : 22$ $1:22$ ?
- (13.42) $m$ $\text(m)$
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A scale is the ratio of the size of a model to the actual object it represents.

Quad boxes are used to easily find rates

First, fill up the quad boxes with the three known values and have the unknown value be $x$ $x$ .

Model Actual

$1$ $1$ $22$ $22$

$61$ $61$ $x$ $x$

Next, equate the two columns and solve for $x$ $x$ .

$\frac{1}{22}$ $1/(22)$ $=$ $=$ $\frac{61}{x}$ $(61)/x$

$1 (x)$ $1(x)$ $=$ $=$ $61 (22)$ $61(22)$ Cross multiply

$x$ $x$ $=$ $=$ $1342$ $1342$

Since the given measurement for the model is in $cm$ $\text(cm)$ , this value will be $1342 cm$ $1342 \text(cm)$ .

Finally, convert the centimetres into metres.

$1 metre$ $1 \text(metre)$ $=$ $=$ $100 centimetres$ $100 \text(centimetres)$

$x$ $x$ $=$ $=$ $1342 \times \frac{1}{100}$ $1342xx1/(100)$ $100 c m$ $100cm$ has $2$ $2$ zeroes $∴$ $:.$ move $2$ $2$ decimal places to left

$x$ $x$ $=$ $=$ $\frac{1342}{100}$ $(1342)/(100)$

$=$ $=$ $13.42$ $13.42$

$x = 13.42 m$ $x=13.42 \text(m)$
Question 3 of 3

3. Question
A building plan indicates that the building’s length will be $70 cm$ $70 \text(cm)$ . If the scale is $1 : 50$ $1:50$ , what would the actual length of the building be in metres?
- (35) $m$ $\text(m)$
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A scale is the ratio of the size of a model to the actual object it represents.

Quad boxes are used to easily find rates

First, fill up the quad boxes with the three known values and have the unknown value be $x$ $x$ .

Model Actual

$1$ $1$ $50$ $50$

$70$ $70$ $x$ $x$

Next, equate the two columns and solve for $x$ $x$ .

$\frac{1}{70}$ $1/(70)$ $=$ $=$ $\frac{50}{x}$ $(50)/x$

$1 (x)$ $1(x)$ $=$ $=$ $50 (70)$ $50(70)$ Cross multiply

$x$ $x$ $=$ $=$ $3500$ $3500$

Since the given measurement for the plan is in $cm$ $\text(cm)$ , this value will be $3500 cm$ $3500 \text(cm)$ .

Finally, convert the centimetres into metres.

$1 metre$ $1 \text(metre)$ $=$ $=$ $100 centimetres$ $100 \text(centimetres)$

$x$ $x$ $=$ $=$ $3500 000 \times \frac{1}{100}$ $3500 000xx1/(100)$ $100 c m$ $100cm$ has $2$ $2$ zeroes $∴$ $:.$ move $2$ $2$ decimal places to left

$x$ $x$ $=$ $=$ $\frac{3500}{100}$ $(3500)/(100)$

$=$ $=$ $35$ $35$

$x = 35 m$ $x=35 \text(m)$

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Quiz summary

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2. Question

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3. Question

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Quizzes

$\frac{1}{22}$ $1/(22)$	$=$ $=$	$\frac{61}{x}$ $(61)/x$

$1 (x)$ $1(x)$	$=$ $=$	$61 (22)$ $61(22)$	Cross multiply
$x$ $x$	$=$ $=$	$1342$ $1342$

$x$ $x$	$=$ $=$	$1342 \times \frac{1}{100}$ $1342xx1/(100)$	$100 c m$ $100cm$ has $2$ $2$ zeroes $∴$ $:.$ move $2$ $2$ decimal places to left

$x$ $x$	$=$ $=$	$\frac{1342}{100}$ $(1342)/(100)$

	$=$ $=$	$13.42$ $13.42$

$\frac{1}{70}$ $1/(70)$	$=$ $=$	$\frac{50}{x}$ $(50)/x$

$1 (x)$ $1(x)$	$=$ $=$	$50 (70)$ $50(70)$	Cross multiply
$x$ $x$	$=$ $=$	$3500$ $3500$

$x$ $x$	$=$ $=$	$3500 000 \times \frac{1}{100}$ $3500 000xx1/(100)$	$100 c m$ $100cm$ has $2$ $2$ zeroes $∴$ $:.$ move $2$ $2$ decimal places to left

$x$ $x$	$=$ $=$	$\frac{3500}{100}$ $(3500)/(100)$

	$=$ $=$	$35$ $35$

Model	Actual
$1$ $1$	$22$ $22$
$61$ $61$	$x$ $x$

Model	Actual
$1$ $1$	$50$ $50$
$70$ $70$	$x$ $x$