3j calculating percentage change
change divided by the original value x 100/1
profit = selling price - cost price
loss = cost price - selling price
calculating a percentage change involves the technique of expressing one quantity as a percentage of another (section 3H)
percentage change = change divided by original value x 100%
percentage profit = profit divided by original value x 100%
percentage loss = loss divided by original value x 100%
a calculation error is the difference between an estimated or measured value an an exact actual or given value
percentage error = error divided by actual value x 100%
calculate the percentage change profit/loss when:
solution:
a. $25 becomes $32
profit = $7
% profit = 7/25 x 100/1 = 28%
b. $60 becomes $48
loss = $12
% loss = 12/60 x 100/1%
= 20%
explanation:
profit = $32 - $25
percentage profit = profit/original value x 100%
loss = $60 - $48
percentage loss = loss/original value x 100%
change:
change = 62 - 50 = 12
% change = 12/50 x 100/1
12/1 x 2/1 = 24%
80 - 68 = 12
% change = 12/80 x 100/1 = 120/8 = 15%
work:
$20 becomes $25
25 - 20 = 5
profit = $5
%profit = 5/20 x 100/1 = 25%
$10 becomes $19
19 - 10 = 9
profit = $9
%profit = 9/10 x 100/1 = 90%
$40 becomes $32
32 - 40 = -8
profit = $-8
%profit = -8/40 x 100/1 = -20%
= 20% loss
$72 becomes $54
54-72 = -18
profit = $-18
%profit = -18/72 x 100/1 = -25%
= 25% loss
$20 becomes $36
36-20 = 16
profit = $16
%profit = 16/20 x 100/1 = 80%
= 80% profit
$10 becomes $13
13-10 = 3
profit = $3
%profit = 3/10 x 100/1 = 30%
= 30% profit
$40 becomes $30
30-40 = -10
profit = $-10
%profit = -10/40 x 100/1 = 25%
= 25% loss
$25 becomes $21
21-25 = -4
profit = $-4
%profit = -4/25 x 100/1 = -16%
= 16% loss
$12 becomes $20
20-12 = 8
profit = $8
%profit = 8/12 x 100/1 = 66 2/3%
= 66% 2/3 profit
$8 becomes $11
11-8 = 3
profit = $3
%profit = 3/8 x 100/1 = 37.5
= 37.5% profit
15g becomes 18g
18-15 = 3
profit = 3g
%profit = 3/15 x 100/1 = 20g
= 20% increase
18kg becomes 15kg
15-1 8= -3
profit = 3kg
%profit = 3/18 x 100/1 = 16 2/3
= 16 2/3 decrease
4m becomes 24m
24-4 = 20
profit = 20m
%profit = 20/4 x 100/1 = 500
= 500% increase
12cm becomes 30cm
30-12 = 18
profit = 18cm
%profit = 18/12 x 100/1 = 150
= 150% increase
a town of 4000 becomes a town of 5000
4000-5000 = -1000
profit = -1000
%profit = 1000/4000 x 100/1 = 250
= 25% increase
a city of 750 000 becomes a city of 900 000
750,000-900,000 = -150,000
profit = -150,000
%profit = 150,000/750,000 x 100/1 = 20%
= 20% increase
a country of 5 000 000 becomes a country of 12 000 000
5,000,000-12,000,000 = -7,000,000
profit = -7,000,000
%profit = 7,000,000/5,000,000 x 100/1 = 140
= 140% increase
a region of 10 000 becomes 7500
10,000-7500 = 2500
profit = 2500
%profit = 2500/10000 x 100/1 = 25
= 25% decrease
note; use the formula: percentage error = error divided by actual value x 100%
albert measures the length of a piece of timber at 24cm which is actually 25cm
24-25 = 1
profit = 1
%profit = 1/25 x 100/1 = 4.166667
= 4%
sally measures the weight of a bowl of flour at 150g which is actually 160g
150-160 = -10
profit = -10
%profit = -10/160 x 100/1 - 6.25
= 6.25
annette records a 100m race time at 15.5 seconds against the actual time of 15.4 seconds (round to one decimal place)
15.5-15.4 = 0.1
profit = 0.1
%profit = 0.1/15.4 x 100/1 = -0.649
= 0.6
kevin records a towns population as 5300 when the actual population is 5327. (round to one decimal point)
5300-5327 = -27
profit = -27
%profit = -27/5327 x 100/1 = -0.5
= -0.5
gari buys a ticket to a concert for $90 but is unable to go she sells it to her friend for $72 calculate the percentage loss gari made
90-72 = 18
profit = 18
%profit = 18/90 x 100/1 = 20
= 20% loss
estelle purchased a piece of sporting memorabilia for $120 twenty years later she sold it for $900 calculate the percentage profit estelle made
120-900 = -780
profit = -780
%profit = -780/120 x 100/1 = -650
= 650% profit
xavier purchased materials for $48 and made a dog kennel he later sold the kennel for $84
48-84 = -36
profit = -36
%profit = -36/48 x 100/1 = -75
= 75% profit
money made = 36
percentage profit = 75%
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