Question

The ratio of Adams books to Brandon's books is 5:4. The ratio of Brandon's books to Colins books is 3:2. Colin has 56 books. How many books does Adam have?

Answer 1

We have two ratios :

Adam : Brandon

5 : 4

Brandon : Colins

3 : 2

The common term between these two ratios is Brandon.

We need to find the ratio of their books together in the form :

a : b : c

To do this, the common term must be the same.

If we multiply the first ratio by 3

and the second ratio by 4

it will be :

5 : 4 => 5(3) : 4(3) = 15 : 12

3 : 2 => 3(4) : 2(4) = 12 : 8

Now we have

15 : 12 and 12 : 8

Since Brandon's ratio is now the same we can express them as :

Adam : Brandon : Colin = 15 : 12 : 8

From the problem, Colin has 56 books

To find the number of Adam's books

Divide the number of Colin's book by its ratio then multiply it by the ratio of Adam

Ratio of Colin = 8

Ratio of Adam = 15

So it will be :

`\begin{gathered} (56)/(8)*15=7*15 \\ =105 \end{gathered}`

Therefore, the correct answer is 105 books