Question

The Lake Smith basketball team had a team picture taken of the players, the coaches, and the trophies from the season. The picture was 4 inches by 6 inches. The team decided to have the picture enlarged to a poster and then enlarged again to a banner measuring 48 inches by 72 inches.

If the scale factor from the picture to the poster is 500%, find the dimensions of the poster.
What scale factor, as a percent, is used to create the banner from the picture?
What percent of the area of the picture is the area of the poster?
Assume you started with the banner and wanted to reduce it to the size of the poster.
What would the scale factor as a percent be?

Answer 1

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Answer:

• poster dimensions: 20 inches by 30 inches
• banner/picture scale factor: 1200%
• poster/picture area ratio: 2500%
• poster/banner reduction ratio: 41.67%

Explanation:

a) Poster dimensions are 500% of the picture dimensions:

500% · 4 in = 500/100 · 4 in = 5 · 4 in = 20 in

5 · 6 in = 30 in

The poster is 40 in by 30 in.

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b) The ratio of banner sized to picture size can be found from the ratio of the smaller dimensions:

48 in/(4 in) = 12 = 12 · 100% = 1200%

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c) The poster/picture area ratio is the square of the scale factor:

poster area/picture area = (500%)^2 = (500/100)^2 = 25

= 25 · 100% = 2500%

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d) The poster/banner reduction ratio is ...

20 in/48 in = 5/12 ≈ 0.4167 = 0.4167 · 100% = 41.67%

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Additional comment

To convert a number or fraction to a percentage, multiply by 100%. To convert a percentage to a number, divide by 100%, or recognize that "%" means "/100". (As above, 500% = 500/100 = 5.)