ratio word problem

[juliag]

here's the question: Jill deceided to enlarge a photograph that measures 5" wide by 7" long into a poster size photograph with a perimeter of 168 inches. The new photo will maintain the same width-to-length ratio. What will the length and width be?

I think this is what I need to do but the answer is not right. HELP

5/7 = x/168-x

Am I on the right track?

 

[Deleted member 4993]

here's the question: Jill deceided to enlarge a photograph that measures 5" wide by 7" long into a poster size photograph with a perimeter of 168 inches. The new photo will maintain the same width-to-length ratio. What will the length and width be?

I think this is what I need to do but the answer is not right. HELP

5/7 = x/168-x

Am I on the right track? Not quite!!

It is a ratio problem - but needs to be dealt differently. One of the ways to solve this would be:

Let the amount of magnification = M

Then

the new length = 7 * M........................... (1)

the new width = 5 * M........................... (2)

New Perimeter = P = 2*(7M + 5M)

we know that P = 168

then

168 = 2*(7M + 5M)............................. (3)

Solve for 'M' from (3) - then use (1) and (2) to get the new length and width.

 

[soroban]

Hello, juliag!

Jill deceided to enlarge a photograph that measures 5" wide by 7" long into a poster size photograph with a perimeter of 168 inches.
The new photo will maintain the same width-to-length ratio. What will the length and width be?

The original photograph is \(\displaystyle 5\times7\) inches.

          5
      * - - - *
      |       |
    7 |       | 7
      |       |
      * - - - *
          5

The poster will be \(\displaystyle 5a \times 7a\) inches
. . and have a perimeter of 168 inches.

            5a
      * - - - - - - *
      |             |
      |             |
   7a |             | 7a
      |             |
      |             |
      |             |
      * - - - - - - *
           5a

The perimeter is: .\(\displaystyle 7a + 5a + 7a + 5a \,=\,24a\) inches
. . and will equal 168 inches.

Can you finish the problem now?