If the blueprint is drawn to scale so that every 1⁄2 inch represents 10 yds, what are the dimensions on the blueprint?

Question

A school is considering adding another student parking lot. The dimensions of the area where the parking lot is to be constructed is 50 yds by 30 yds.

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Answer 1 · 2018-06-03T21:58:51

See a solution process below:

The scale is:

$\frac{1}{2} in = 10 yds$ $1/2"in" = 10"yds"$

We can first multiply the equation for scale by $5$ $color(red)(5)$ to get one dimension of the blue print:

$5 \times \frac{1}{2} in = 5 \times 10 yds$ $color(red)(5) xx 1/2"in" = color(red)(5) xx 10"yds"$

$\frac{5}{2} in = 50 yds$ $5/2"in" = 50"yds"$

Or

$2 \frac{1}{2} in = 50 yds$ $2 1/2"in" = 50"yds"$

We can next multiply the equation for scale by $3$ $color(red)(3)$ to get the other dimension of the blue print:

$3 \times \frac{1}{2} in = 3 \times 10 yds$ $color(red)(3) xx 1/2"in" = color(red)(3) xx 10"yds"$

$\frac{3}{2} in = 30 yds$ $3/2"in" = 30"yds"$

Or

$1 \frac{1}{2} in = 30 yds$ $1 1/2"in" = 30"yds"$

The dimension of the portion of the blue print showing the new student parking lot would be:

$2 \frac{1}{2} inches by 1 \frac{1}{2} inches$ $2 1/2" inches by "1 1/2" inches"$