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OlympiadBench / 2315 / Digital images consist of a very large number of equally spaced dots called…

Problem

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question

Digital images consist of a very large number of equally spaced dots called pixels The resolution of an image is the number of pixels/cm in each of the horizontal and vertical directions. Thus, an image with dimensions $10 \mathrm{~cm}$ by $15 \mathrm{~cm}$ and a resolution of 75 pixels/cm has a total of

(10 \times 75) \times(15 \times 75)=843750

pixels. If each of these dimensions was increased by

n \%

and the resolution was decreased by

n \%

, the image would have 345600 pixels. Determine the value of

n

Plain-text mathematical notation (without MathML)

Digital images consist of a very large number of equally spaced dots called pixels The resolution of an image is the number of pixels/cm in each of the horizontal and vertical directions.

Thus, an image with dimensions $10 \mathrm{~cm}$ by $15 \mathrm{~cm}$ and a resolution of 75 pixels/cm has a total of (10×75)×(15×75)=843750 pixels.

If each of these dimensions was increased by n% and the resolution was decreased by n%, the image would have 345600 pixels.

Determine the value of n.

Original LaTeX notation

Digital images consist of a very large number of equally spaced dots called pixels The resolution of an image is the number of pixels/cm in each of the horizontal and vertical directions.

Thus, an image with dimensions $10 \mathrm{~cm}$ by $15 \mathrm{~cm}$ and a resolution of 75 pixels/cm has a total of $(10 \times 75) \times(15 \times 75)=843750$ pixels.

If each of these dimensions was increased by $n \%$ and the resolution was decreased by $n \%$, the image would have 345600 pixels.

Determine the value of $n$.

answer type

Numerical

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2315
task_id: b701434e-03de-5b60-a699-6503fa7ac932
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2315
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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