Percent of Change
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SAT Math › Percent of Change
On Monday, the price of a shirt costs x dollars. On Tuesday, the manager puts the shirt on sale for 10% off Monday's price. On Wednesday, the manager increases the price of the shirt by 10% of Tuesday's price. Describe the change in price from Monday to Wednesday.
No change
10% increase
10% decrease
1% increase
1% decrease
Explanation
To find the cost on Tuesday, take 10% off Monday's price. In other words, find 90% of Monday's price. This is simply 0.9_x_. If we are to now add 10% of this value back onto itself to find Wednesday's price, we want 100% + 10%, or 110% of 0.9_x_.
1.1(0.9_x_) = 0.99_x_
This value is 1% smaller than x.
On Monday, the price of a shirt costs x dollars. On Tuesday, the manager puts the shirt on sale for 10% off Monday's price. On Wednesday, the manager increases the price of the shirt by 10% of Tuesday's price. Describe the change in price from Monday to Wednesday.
No change
10% increase
10% decrease
1% increase
1% decrease
Explanation
To find the cost on Tuesday, take 10% off Monday's price. In other words, find 90% of Monday's price. This is simply 0.9_x_. If we are to now add 10% of this value back onto itself to find Wednesday's price, we want 100% + 10%, or 110% of 0.9_x_.
1.1(0.9_x_) = 0.99_x_
This value is 1% smaller than x.
Phoenicia is a grocery store that is expanding quickly.
In 2011 Phoenicia's total sales were $1,800,800.
In 2012 their sales rose to $2,130,346.
By what percentage did the store increase its income from 2011 to 2012.
(Round answer to the nearest tenth.)
18.3%
19.2%
16.4%
21.0%
10.5%
Explanation
$1,800,800 divided by 100 equals 18,008 and $2,130,346 divided by 18,008 is 118.3
So we know that $2,130,346 is 118.3% of the sales in the previous year. Hence sales increased by 18.3%.
If the side of a square is doubled in length, what is the percentage increase in area?
Explanation
The area of a square is given by 
If the side of a square is doubled in length, what is the percentage increase in area?
Explanation
The area of a square is given by
Phoenicia is a grocery store that is expanding quickly.
In 2011 Phoenicia's total sales were $1,800,800.
In 2012 their sales rose to $2,130,346.
By what percentage did the store increase its income from 2011 to 2012.
(Round answer to the nearest tenth.)
18.3%
19.2%
16.4%
21.0%
10.5%
Explanation
$1,800,800 divided by 100 equals 18,008 and $2,130,346 divided by 18,008 is 118.3
So we know that $2,130,346 is 118.3% of the sales in the previous year. Hence sales increased by 18.3%.
If the length of a rectangle is increased by thirty percent, which of the following most closely approximates the percent by which the rectangle's width must decrease, so that the area of the rectangle remains unchanged?
17
21
23
25
30
Explanation
The cost of a hat increases by 15% and then decreases by 35%. After the two price changes, the new price of the hat is what percent of the original?
80%
85.3%
75%
88.91%
74.75%
Explanation
The easiest way to do percentage changes is to keep them all in one equation. Therefore, we would say that an increase of 15% is the same as multiplying the original value by 1.15. Likewise, we would say that a discount by 35% is the same as multiplying the original by .65.
For our problem, let the hat cost X dollars originally. Therefore, after its increase, it costs 1.15_X_ dollars. Now, we can consider this new price as the whole to which the discount will be applied. Therefore, a 35% reduction is (1.15_X_) * 0.65.
Simplifying, we get 0.7475, or 74.75%.
If the price of a TV was decreased from $3,000 to $1,800, by what percent was the price decreased?
20%
30%
40%
50%
60%
Explanation
The price was lowered by $1,200 which is 40% of $3,000.
If the length of a rectangle is increased by thirty percent, which of the following most closely approximates the percent by which the rectangle's width must decrease, so that the area of the rectangle remains unchanged?
17
21
23
25
30
Explanation