# Anna has three cats named Molly, Dolly and Kate. Molly's and Dolly's weight ratio is 4:5 while Dolly's and Kate's weight ratio is 6:7. What is the weight ratio between Molly and Kate?

May 31, 2018

$\text{Molly" \ : \ "Kate} = 24 : 35$

#### Explanation:

The weight ratios given are as given below,

• $\text{Molly" : "Dolly} = 4 : 5$
• $\text{Dolly" : "Kate} = 6 : 7$

In order to get a common weight for Dolly, in both of the above ratios, multiply by $\frac{5}{6}$. So

$\text{Dolly" : "Kate} = \left(6 \times \frac{5}{6}\right) : \left(7 \times \frac{5}{6}\right)$

$\text{Dolly" : "Kate} = 5 : \frac{35}{6}$

Now, considering the weight of all the three cats into a ratio

$\text{Molly" : "Dolly" : "Kate} = 4 : 5 : \frac{35}{6}$

the conversion of the ratio into an integer form,

$\text{Molly" : "Dolly" : "Kate} = \left(\frac{4}{1} \times \frac{6}{6}\right) : \left(\frac{5}{1} \times \frac{6}{6}\right) : \left(\frac{35}{6}\right)$

$\text{Molly" : "Dolly" : "Kate} = \left(\frac{24}{6}\right) : \left(\frac{30}{6}\right) : \left(\frac{35}{6}\right)$

So

$\text{Molly" : "Dolly" : "Kate} = 24 : 30 : 35$

Therefore, the weight ratio of $\text{Molly" : "Kate} = 24 : 35$