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Sub 505 (Easy)|   Geometry|   Word Problems|            
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If a rectangular photograph that Is 10 inches wide by 15 inches long Is to be enlarged so that the width will be 22 inches and the ratio of width to length will be unchanged, then the length, in inches, of the enlarged photograph will be

(A) 33
(B) 32
(C) 30
(D) 27
(E) 25

We can solve this question using equivalent ratios

We can use the ratio width/length

Let x = the length of the enlarged photograph

We can write: 10/15 = 22/x
We can save ourselves some time by simplifying the first ratio to get: 2/3 = 22/x
Cross multiply to get: 2x = (3)(22)
Solve: x = 33

Answer: A

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If a rectangular photograph that Is 10 inches wide by 15 inches long Is to be enlarged so that the width will be 22 inches and the ratio of width to length will be unchanged, then the length, in inches, of the enlarged photograph will be

(A) 33

(B) 32

(C) 30

(D) 27

(E) 25
\(10----------2.2---------->22\)

So, \(15----------2.2---------->33\), Answer must be (A)
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To find the length of the enlarged photograph, we need to maintain the ratio of width to length.

The original photograph has a width of 10 inches and a length of 15 inches, resulting in a width-to-length ratio of 10/15 = 2/3.

If we enlarge the width to 22 inches, we need to find the corresponding length that maintains the same ratio.

We can set up a proportion to solve for the length of the enlarged photograph:

10/15 = 22/x
10x = 15 * 22 = 330
x = 330/10 = 33

Therefore, the length of the enlarged photograph will be 33 inches, which corresponds to option (A).
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