Kelly enlarged the area of a photograph to 250% of its original size. The original dimensions of the photograph were 5 inches by 7 inches. What is the area of the enlarged photograph, in square inches?
I know the solution is 5(2.5) times 7(2.5) but it says she enlarged the area by 250 percent. so shouldn't it be 2.5 (35)?
Also when do we know when to add 100% to a percent or keep it as the percent like this question? please help
Depends.
If, as stated, the area grew to 250%, then it becomes 2.5(35)
If both length and width were magnified by a factor of 2.5, then yes, 5(2.5) * 7(2.5) = 35 * 2.5^2
you are correct
when something is "increased by" 20%, that means it has an extra 20%, or 1.2 times its value
when they give you an actual size factor, there's no additional 100% to add.
Many people get these confused, so make sure to read the question carefully.
Also, the "solution" you cite would be correct if the photograph had been enlarged by a factor of 250%. In that case, it usually means that each dimension is increased, not the area. So your analysis is correct, if the question was worded correctly.
Oh so since it's the area then it would have to be 5(2.5) times 7(2.5) ?
To find the area of the enlarged photograph, you need to calculate the area of the original photograph and then multiply it by the enlargement factor.
The original dimensions of the photograph are 5 inches by 7 inches, so the original area is 5 inches * 7 inches = 35 square inches.
To enlarge the photograph by 250%, you need to increase each dimension by 250% or 2.5 times its original value. Multiplying the original dimensions by 2.5 gives you the enlarged dimensions: 5 inches * 2.5 = 12.5 inches and 7 inches * 2.5 = 17.5 inches.
Now, to find the area of the enlarged photograph, multiply the enlarged dimensions together: 12.5 inches * 17.5 inches = 218.75 square inches.
So, the area of the enlarged photograph is approximately 218.75 square inches.
To address your question about adding or keeping percentages, when a percentage refers to an increase or a decrease, you generally need to add or subtract the percentage from the original value. In this case, since the question states that the photograph was enlarged by 250%, we need to increase each dimension by 250% or 2.5 times its original value. However, if the question asked for a 250% increase instead of an enlargement of 250%, you would simply add 250% to the original value.