Question

Leah's house has a media room with a large flat-screen television to watch movies. The media room television has a width of 8 feet and a height of 4.5 feet.

The flat-screen television in Leah's living room has a height of 27 inches and has the same width to height ratio as the media room television. What is the width of Leah's living room television?
A.
15 inches
B.
32 inches
C.
64 inches
D.
48 inches

Answer 1

We need to convert that ratio to a format with whole numbers for convenience's sake. To do that, let's multiply that decimal by 2 since it's half of an odd number (ratio is in fraction form so you can understand):\[\frac{8\times2}{4.5\times2}=\frac{16}{9}\]Your new ratio is \(16:9\) for the media room television.

Answer 2

Sorry -- had an error where I deleted some of my responses. The ratio originally started out as \(8:4.5\) in width-to-height ratio, but you need to change it to a whole-number format to get this to work out in a way you can easily solve.

Answer 3

Anyway, this is in feet but the measurement given for the other television is in inches. So we have to convert this ratio to inches form, and 1 foot is 12 inches, so:\[\frac{16\cdot12}{9\cdot12}=\frac{192}{108}\]
...or you can just use \(\frac{16}{9}\) because this is a ratio!
TL;DR this step is unnecessary, but if you're paranoid you can always do it and then simplify again.

Now we have to find the width of the flat-screen television, which we'll make \(x\) for convenience sake. And to find the value we have to set the two ratios equal to each other in what's called a \(proportion.\)

Answer 4

The ratio format for the flat-screen television, height-to-width, is as follows:\[\frac{x}{27}\]Now we set this equal to the basic ratio for the media room television:\[\frac{16}{9}=\frac{x}{27}\]To solve for \(x\) we will cross multiply.\[9\cdot x=27\cdot16\]And now we will have a variable expression: \(9x=27\cdot16=432\)

Answer 5

To find the width of the media room television, \(x\), you just have to isolate the variable. To do this, divide both sides by 9:\[\frac{\cancel{9}{x}}{\cancel{\color{orchid}{9}}}=\frac{432}{\color{orchid}{9}}\]\[x=432\div9=48\]You have a flat-screen television with a width of \(\color{green}{48\text{ inches}}\).