Question

The heights of Russian dolls are in the ratio 4 : 6 : 7



In a set of dolls, the height of the middle doll is 9 cm.

What are the heights of the other dolls?

Answer 1

The ratio has three quantities. In this case, we use a property of ratios.

Property of ratios: The ratios equal after any number is multiplied. The number should not equal 0.

Solving

Let's multiply by a not known number $x$.

$4:6:7=4x:6x:7x$

The number of three dolls are $4x$, $6x$, and $7x$.

So, the height of the middle doll is $6x=9$.

Then $x=\dfrac{3}{2}$ is multiplied to the ratio.

$4:6:7=6:9:\dfrac{21}{2}$

The heights of the other dolls are $6$ cm and $\dfrac{21}{2}$ cm.

More information:

• Two ratios having two numbers. For example, $a:b=c:d$.

The means and extremes are used when two ratios having two numbers are proportional.

• Two ratios having more than two numbers.

We multiply by a not known number to the ratios. (This doesn't change the ratio.)

Answer 2

Question= The heights of Russian dolls are in the ratio 4 : 6 : 7

In a set of dolls, the height of the middle doll is 9 cm.

What are the heights of the other dolls?

To find:

What are the heights of the other dolls?

Solution:

Let s be the smallest, m be the middle, and t be the tallest.

a)

s:9 = 4:6 => s = 6

t :9 = 7:6 => t = 21/2

6 cm ....9 cm ....21/2 cm

b)

s:9 = 4:7 => s = 36/7

m:9 = 6:7 => m = 54/7

36/7 cm ....54/7 cm ....9 cm