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Question 1 of 3
After a 20% price rise, a smartphone is now worth $600. What was its original price?
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First, use a rectangle and list down the values: percentages on the left side and amounts on the right side.
New price=$600
Percentage of original price=100%
Percentage of new price=100+20=120%
Original price=?
1% Method -Unitary Method
For this method, find 1% of the original amount by dividing both known values by 120.
120% |
= |
$600 |
|
120÷120 |
= |
600÷120 |
Divide both sides by 120 |
1 |
= |
5 |
Hence, 1% of the original amount is $5.
To find the original price, which is 100% of the value, multiply the 1% value, which is 5, by 100.
Hence, the original price of the smartphone was $500_
Proportion Method
To find the missing value, cross-multiply the fraction of the percentages by the fraction of the given and total value.
Let the original price be x
120100 |
= |
600x |
|
120×x |
= |
600×100 |
Cross multiply |
120x |
= |
60,000 |
120x÷120 |
= |
60,000÷120 |
Divide both sides by 120 |
|
x |
= |
600012 |
Simplify |
|
x |
= |
500 |
Hence, the original price of the smartphone was $500_
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Question 2 of 3
A carpenter charges $990 for his work, which includes a 10% tax. How much does the carpenter originally charge?
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First, use a rectangle and list down the values: percentages on the left side and amounts on the right side.
Price with tax=$990
Percentage of price without tax=100%
Percentage of price with tax=100+10=110%
Price without tax=?
1% Method -Unitary Method
For this method, find 1% of the original amount by dividing both known values by 110.
110% |
= |
$990 |
|
110÷110 |
= |
990÷110 |
Divide both sides by 110 |
1 |
= |
9 |
Hence, 1% of the original amount is $9.
To find the original price, which is 100% of the value, multiply the 1% value, which is 9, by 100.
Hence, the original charge is $900_
Proportion Method
To find the missing value, cross-multiply the fraction of the percentages by the fraction of the given and total value.
Let the original price be x
110100 |
= |
990x |
|
110×x |
= |
990×100 |
Cross multiply |
110x |
= |
99,000 |
110x÷110 |
= |
99,000÷110 |
Divide both sides by 110 |
|
x |
= |
990011 |
Simplify |
|
x |
= |
900 |
Hence, the original charge is $900_
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Question 3 of 3
After a 12.5% discount, a bed is now worth $730. What was its original price?
Round to the nearest dollar amount
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First, use a rectangle and list down the values: percentages on the left side and amounts on the right side.
New price=$730
Percentage of original price=100%
Percentage of new price=100-12.5=87.5%
Original price=?
1% Method -Unitary Method
For this method, find 1% of the original amount by dividing both known values by 87.5.
87.5% |
= |
$730 |
|
87.5÷87.5 |
= |
730÷87.5 |
Divide both sides by 87.5 |
1 |
= |
8.3429 |
Rounded to four decimal places |
Hence, 1% of the original amount is $8.3429.
To find the original amount, which is 100% of the value, multiply the 1% value, which is 8.3429, by 100.
100% |
= |
8.3429×100 |
|
= |
834.29 |
|
= |
834 |
Round to the nearest whole number |
Hence, the original price of the bed was $834_
Proportion Method
To find the missing value, cross-multiply the fraction of the percentages by the fraction of the given and total value.
Let the original price be x
87.5100 |
= |
730x |
|
87.5×x |
= |
730×100 |
Cross multiply |
87.5x |
= |
73,000 |
87.5x÷87.5 |
= |
73,000÷87.5 |
Divide both sides by 87.5 |
|
x |
= |
834.28571 |
x |
= |
834 |
Round to the nearest whole number |
Hence, the original price of the bed was $834_