the actual length of the living room

Question

On the blueprint of a house, 24 millimeters represents 5 meters. The length of the living room is 30 millimeters on the blue print.what is the actual length of the living room?

Answer 1

Hi Shenel!

There are a couple ways to set up a scaling or ratios problem. Regardless, ratios are often written like fractions. I'll describe the process and also show you below.

On the left, let's put 24mm on top (the numerator) and 5m on bottom (the denominator). To solve the ratio, we set this left side of the equation equal to a right. The right side will have 30mm on top. We want the units, in this case mm, on top to match. On bottom right side, we will insert a variable to answer "what is the actual length of the living room?" and we can use whatever letter we want to stand for this variable, as you know. Let's use x, and solve for x.

Note that our final answer will be in units of m, or meters. Just as we want our numerator units to match, we also want our bottom denominator units to match. We can include units in the beginning to ensure correct set up of the problem. My preference is to disregard them during the computation and include the proper units with my final answer.

(24mm)/(5m) = (30mm)/(x)
(24)/(5) = (30)/(x)

Look at fractions as division. The opposite of division is multiplication. We multiply the left and right sides by 5. We also multiply the left and rights sides by x. We simplify.

(5)(x)(24)/(5) = (5)(x)(30)/(x)
24x = 150
x = 6.25

x = 6.25 meters
(round as instructed by teacher)

Hope that helps.

Answer 2

Assuming that x represents mm and y represents m, then:

24x = 5y. Solve for x to determine what one millimeter represents in meters.

x=5y/24

Therefore, 1 millimeter = 5/24 meters.

If the living room is 30 mm, then:

30x = 5y/24 Solve for x to determine how many mm.

x= (5(30)/24) meters

x=150/24 meters

x = 6.25 meters.

 

 

 

Answer 3

you can set up a proportion

24 mm/5 m=30 mm/ ? m

24/5=30/n

cross multiply

24*n=5*30

24n=150

n=150/24

n=6.25 m

or,...

24 mm/5 m=4.8 mm equals 1 m

30/4.8=6.25 m again