© t madas finding the amount before a percentage change
TRANSCRIPT
© T Madas
Findingthe amountbefore aPercentageChange
© T Madas
The value of a painting went up by 25% and is now valued at £400.
What was its value before the increase?
The answer IS NOT £400 less 25%,
WHY?
If you increase £300 by 25% you get
i.e. £300
£375
Why doesn’t a decrease by 25% get balanced by an increase of 25%?
How do we solve a problem like this?
© T Madas
Value
Before400
x 1.25
£320 400÷ 1.25
The value of a painting went up by 25% and is now valued at £400.
What was its value before the increase?
© T Madas
An item costs £282 after V.A.T at 17.5%.What is its price before V.A.T?
This formal equation set up shows why this method works but it is not strictly required
b 1.175´ 282= Û1.175b 282=
b = 2821.175
ÛÛ
240b =
b
£240
x 1.175
÷ 1.175
£282
© T Madas
An item costs £93.50 after a 15% discount.What did it cost before the discount?
b 0.85´ 93.5= Û
0.85b 93.5=
b = 93.50.85
ÛÛ
110b =
b
£110
x 0.85
÷ 0.85
£93.50
© T Madas
Find the number which was increased by 12% to give 420.
b 1.12´ 420= Û
1.12b 420=
b = 4201.12
ÛÛ
375b =
b
375
x 1.12
÷ 1.12
420
© T Madas
Find the number which was decreased by 17% to give 415.
b 0.83´ 415= Û
0.83b 415=
b = 4150.83
ÛÛ
500b =
b
500
x 0.83
÷ 0.83
415
© T Madas
Finding the amount before a percentage increase or decrease:
Take the final amount and divide it by the appropriate percentage multiplier
Find the number that was increased by 30% to give 520
520 ÷ 1.3 = 400
Find the number that was decreased by 30% to give 420
420 ÷ 0.7 = 600
Finding the amount after a percentage increase or decrease:
Take the original amount and multiply it, by the appropriate percentage multiplier
Increase 500 by 15%
500 x 1.15 = 575
Decrease 700 by 11%
700 x 0.89 = 623
Percentage Multiplier SummaryPercentage Multiplier Summary
© T Madas
Practiceon findingthe amount
before aPercentageChangeusing acalculator
© T Madas
What number was increased by 10% to give 121?
110
Amounts Before Percentage Changes
What number was increased by 15% to give 184?
160
What number was increased by 12% to give 252?
225
What number was increased by 27% to give 406.4?
320
What number was decreased by 10% to give 468?
520
What number was decreased by 25% to give 273?
364
What number was decreased by 40% to give 252?
420
What number was decreased by 11% to give 534?
600
© T Madas
What number was increased by 12% to give 140?
125
What number was decreased by 12% to give 484?
550
What number was increased by 17.5% to give 282?
240
What number was decreased by 17.5% to give 660?
800
What number was increased by 5.5% to give 147.7?
140
What number was decreased by 5.5% to give 1701?
1800
What number was increased by 1% to give 343.4?
340
What number was decreased by 1% to give 742.5?
750
Amounts Before Percentage Changes
© T Madas
110% of a number is 121. What is the number?
110
115% of a number is 184. What is the number?
160
112% of a number is 252. What is the number?
225
127% of a number is 406.4. What is the number?
320
90% of a number is 468. What is the number?
520
75% of a number is 273. What is the number?
364
60% of a number is 252. What is the number?
420
89% of a number is 534. What is the number? 600
Amounts Before Percentage Changes
© T Madas
112% of a number is 140. What is the number?
125
88% of a number is 484. What is the number? 550
117.5% of a number is 282. What is the number?
240
87.5% of a number is 700. What is the number? 800
105.5% of a number is 147.7. What is the number?
140
94.5% of a number is 1701. What is the number?
1800
101% of a number is 343.4. What is the number?
340
99% of a number is 742.5. What is the number?
750
Amounts Before Percentage Changes
© T Madas
Teston findingthe amount
before aPercentageChangeusing acalculator
© T Madas
What number was increased by 10% to give 121?
110
Amounts Before Percentage Changes
What number was increased by 15% to give 184?
160
What number was increased by 12% to give 252?
225
What number was increased by 27% to give 406.4?
320
What number was decreased by 10% to give 468?
520
What number was decreased by 25% to give 273?
364
What number was decreased by 40% to give 252?
420
What number was decreased by 11% to give 534?
600
© T Madas
What number was increased by 12% to give 140?
125
What number was decreased by 12% to give 484?
550
What number was increased by 17.5% to give 282?
240
What number was decreased by 17.5% to give 660?
800
What number was increased by 5.5% to give 147.7?
140
What number was decreased by 5.5% to give 1701?
1800
What number was increased by 1% to give 343.4?
340
What number was decreased by 1% to give 742.5?
750
Amounts Before Percentage Changes
© T Madas
110% of a number is 121. What is the number?
110
115% of a number is 184. What is the number?
160
112% of a number is 252. What is the number?
225
127% of a number is 406.4. What is the number?
320
90% of a number is 468. What is the number?
520
75% of a number is 273. What is the number?
364
60% of a number is 252. What is the number?
420
89% of a number is 534. What is the number? 600
Amounts Before Percentage Changes
© T Madas
112% of a number is 140. What is the number?
125
88% of a number is 484. What is the number? 550
117.5% of a number is 282. What is the number?
240
87.5% of a number is 700. What is the number? 800
105.5% of a number is 147.7. What is the number?
140
94.5% of a number is 1701. What is the number?
1800
101% of a number is 343.4. What is the number?
340
99% of a number is 742.5. What is the number?
750
Amounts Before Percentage Changes
© T Madas