# Math Help - Need help in Ratios

1. ## Need help in Ratios

Q#1
Building hallway is 23.5 inches long.
The scale is 3.25 inches = 14 feet. How long is the hallway??

Q#2
Drawing with a scale of 3.75 inches = 13 feet. What distance on the drawing should be used to represent 9 feet 3 inches??

Q#3
On level ground, a street pole casts a shadow 10.7 m long. At the same time, a tree 25.0 m high casts a shadon 35.0 m long. How high is the pole?
I tried this, but my number is way to small.

Q#4
On a map, 8cm = 50 km. What is the distance between the two cities if the distance between them on the map is 13.6cm.
Actual distance in km??

Thanks for your help, and explain fully so I can understand.

2. ## Ratios and multiplying factors

Q#1
Building hallway is 23.5 inches long.
The scale is 3.25 inches = 14 feet. How long is the hallway??

Q#2
Drawing with a scale of 3.75 inches = 13 feet. What distance on the drawing should be used to represent 9 feet 3 inches??

Q#3
On level ground, a street pole casts a shadow 10.7 m long. At the same time, a tree 25.0 m high casts a shadon 35.0 m long. How high is the pole?
I tried this, but my number is way to small.

Q#4
On a map, 8cm = 50 km. What is the distance between the two cities if the distance between them on the map is 13.6cm.
Actual distance in km??

Thanks for your help, and explain fully so I can understand.
There are two important things that you need to learn to do when dealing with maps and plans. They are:

First, in questions like this, change the scale that you've been given so that both bits are in the same units. So, for instance, in #1 the scale you're given is:
$3.25$ inches represents $14$ feet
So that's:
$3.25$ inches represents $14 \times 12 = 168$ inches
That's a ratio of:
$3.25 : 168$
Noting that $0.25$ is one-quarter, multiply both numbers in the ratio by $4$ to get rid of decimals. That's:
$3.25 \color{red}\times 4\color{black}:168\color{red}\times 4$
$= 13:672$
This means that $13$ inches (or feet, or whatever) on the plan represents $672$ inches (feet, whatever) on the ground.

Secondly, learn how to make things bigger and smaller using what are called multiplying factors. It's very simple. If you have a ratio
$A:B$
then the multiplying factors are:
$\frac AB$ and $\frac BA$
That's all. There aren't any more.

So with the ratio
$13:672$
the multiplying factors are
$\frac{13}{672}$ and $\frac{672}{13}$
And then all you need to know is, to make a number bigger, use the multiplying factor that has the bigger number on top; to make a number smaller use the one that has the smaller number on top.

OK. Now I'll complete question #1, and see if you can do the others. As we've said, the multiplying factors are:
$\frac{13}{672}$ and $\frac{672}{13}$
On the plan, the hallway is $23.5$ inches. Obviously the real hallway is much bigger than this. So we multiply $23.5$ inches by $\frac{672}{13}$. And the answer is:
$23.5\times \frac{672}{13}$
$=1215$ inches (to the nearest inch)

$= 101$ feet $3$ inches
Now have a go at the others. Let us know if you get stuck.