Units Of Measurement And Applications Worksheet Page 34
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44WORKED EXAMPLE 4
a
John’s weight increased from 64 kg to 68 kg. Find the percentage increase in his weight.
b
The value of a car decreased from $18 500 to $14 900 in 1 year. Calculate the percentage decrease in value.
Solve
Think
Apply
a
Method 1
Method 1
Method 1
Increase = 68 − 64 kg
Percentage increase
Find the increase in weight and
68 − 64
= 4 kg
express this as a percentage of the
_______
=
× 100%
64
Percentage increase
original weight. Percentage increase
= 6.25%
4 ___
increase in quantity
=
× 100% = 6.25%
________________
=
× 100%
64
original quantity
Method 2
Method 2
Method 2
68 ___
68 ___
68 ___
Express the second weight as a
× 100% = 106.25%
=
× 100%
64
64
64
percentage of the fi rst and then
= 106.25%
The increased weight is
subtract 100%. Percentage increase
106.25% of the original weight.
Percentage increase
second quantity
_____________
=
× 100% − 100%
= 106.25% − 100%
Percentage increase
fi rst quantity
= 106.25% − 100% = 6.25%
= 6.25%
b
Method 1
Method 1
Method 1
Decrease = $18 500 − $14 900
Percentage decrease
Find the decrease in value and
18 500 − 14 900
= $3600
express this as a percentage of the
______________
=
× 100%
18 500
Percentage decrease
original value. Percentage decrease
= 19.5% (to 1 decimal place)
3600
______
decrease in value
=
× 100% ≈ 19.5%
______________
=
× 100%
18 500
original value
Method 2
Method 2
Method 2
14 900
14 900
14 900
Express the second value as a
______
______
______
=
× 100%
× 100% ≈ 80.5%
18 500
18 500
18 500
percentage of the fi rst and then
= 80.5% (to 1 decimal place)
The decreased value is 80.5%
subtract this result from 100%.
of the original value.
Percentage decrease
Percentage decrease
= 100% − 80.5%
Percentage decrease
second quantity
_____________
= 100% −
× 100%
= 100% − 80.5% = 19.5%
= 19.5% (to 1 decimal place)
fi rst quantity
12
a
Complete the following to fi nd the percentage increase in weight from 52 kg to 55 kg.
Increase in weight = 55 − ____ kg = ____ kg
□ __
Percentage increase =
× 100 % = ____% = ____% (to 1 decimal place)
□
b
Complete the following to fi nd the percentage decrease in cost from $186 to $154.
Decrease in cost = $____ − $____ = $____
Percentage decrease = ____ × 100 % = ____% =____% (to 1 decimal place)
13
Find the percentage increase (to 1 decimal place) from :
a
b
c
$350 to $425
7.2 m to 7.8 m
63 kg to 68 kg
d
e
f
$80 to $215
4.2 kg to 8.4 kg
480 mL to 530 mL
14
Find the percentage decrease from:
a
b
c
$256 to $190
55 kg to 51 kg
15.8 s to 15.5 s
d
e
f
430 ha to 385 ha
$5400 to $1800
13 s to 12.2 s
INVESTIGATION 2.2
68
Insight Mathematics General 11
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