A photographer has to change the size of his cover photo. He increase the length by 30% and decrease the width by 10%.. By what percent was the area of the final photo changed
Well, let's do some calculations! First, let's assume the original length of the cover photo is L and the original width is W.
After increasing the length by 30%, the new length becomes L + (0.3 * L) = 1.3L.
After decreasing the width by 10%, the new width becomes W - (0.1 * W) = 0.9W.
The area of the original photo is L * W, and the area of the new photo is (1.3L) * (0.9W) = 1.17LW.
To calculate the percent change in area, we can use the formula:
Percent Change = ((New Value - Original Value) / Original Value) * 100.
So, applying the formula to the area, we get:
Percent Change = ((1.17LW - LW) / LW) * 100 = (0.17LW / LW) * 100 = 17%.
Therefore, the area of the final photo changed by 17%.
To find the percent change in the area of the final photo, we need to calculate the individual changes in the length and width, and then calculate the overall change in area as a percentage.
Let's assume the original length of the photo is L and the original width is W.
The new length after increasing it by 30% is:
New length = L + (30% of L) = L + (0.3 * L) = 1.3L
The new width after decreasing it by 10% is:
New width = W - (10% of W) = W - (0.1 * W) = 0.9W
The area of the original photo is:
Original area = Length * Width = L * W
The area of the final photo is:
Final area = New length * New width = 1.3L * 0.9W
Now, we can find the percent change in the area as follows:
Change in area = Final area - Original area
Percent change in area = (Change in area / Original area) * 100
Substituting the values, we have:
Change in area = (1.3L * 0.9W) - (L * W) = 1.17LW - LW = 0.17LW
Percent change in area = (0.17LW / (LW)) * 100 = 17%
Therefore, the area of the final photo changed by 17%.
To find the percent change in area of the final photo, we need to compare the area before and after the changes.
Let's say the original length and width of the photo were L and W, respectively. The original area is given by A = L * W.
After the changes, the new length is increased by 30%, so the new length is 1.3L. Similarly, the new width is decreased by 10%, so the new width is 0.9W.
The new area, A', is given by A' = (1.3L) * (0.9W) = 1.17LW.
To find the percent change in area, we can use the formula:
Percent change = ((A' - A) / A) * 100
Substituting the values, we get:
Percent change = ((1.17LW - LW) / LW) * 100
Simplifying:
Percent change = (0.17LW / LW) * 100
The L and W cancels out:
Percent change = 0.17 * 100
Therefore, the area of the final photo was changed by 17%.
To solve the problem, we can use the formula:
Final Area = (1 + Percent Increase/100) x (1 - Percent Decrease/100) x Original Area
Let's say the original length and width of the photo were L and W, respectively, so the original area was:
Original Area = L x W
After increasing the length by 30%, the new length becomes:
New Length = L + 0.3L = 1.3L
After decreasing the width by 10%, the new width becomes:
New Width = W - 0.1W = 0.9W
So the final area becomes:
Final Area = 1.3L x 0.9W = 1.17LW
The percent change in area can be calculated as:
Percent Change in Area = ((Final Area - Original Area) / Original Area) x 100%
Substituting the values, we get:
Percent Change in Area = ((1.17LW - LW) / LW) x 100%
Percent Change in Area = (0.17LW / LW) x 100%
Percent Change in Area = 17%
Therefore, the area of the final photo changed by 17%.