How did I get this wrong?

Question

If the length of each of the sides of three square garden plots is increased by 50 percent, by what percent is the sum of the areas of the three plots increased? 125%, is the right answer, but I got this one wrong.
I assigned the value of 2 to the original sides
2x2=4, 4x3=12
raising those values 50%
3x3=9, 9x3=27
27/12=2.25
whish is not 125% no matter how I try to twist it

? · Accepted Answer

All the steps you did were right
But you just got confused on what you have to find

You have to find the percentage increase not the ratio between the new area and the old area

So your answer will be, ((27-12)/12)*100 = 125 %

Blake S · Answer

Here's how I'd look at it:
Assign the original length of the garden as x. 
Original Area: 3xÂ²

Now we increase the length of each side by 50%
50% of x is x/2
x + x/2 = 3x/2

New area: 
(3x/2)Â² * 3
= 9xÂ²/4 * 3
= 27xÂ²/4

Now find the percent increase:
|New_Value - Old_Value| / Old_Value * 100
[(27xÂ²/4 - 3xÂ²) / 3xÂ²] * 100
(9/4 - 1) * 100
5/4 * 100
1.25 * 100
125%

The thing you were forgetting was that the percent increase is calculated by subtracting the old value from the new value before you divide by the old value. 

Hope this helps! :)

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How did I get this wrong?

2 Answers