Question

Alex and Freddy collect stamps.

The number of stamps in Alex’s collection is in ratio $3:5$ to the number of stamps in Freddy’s collection.

If Freddy gives Alex $10$ stamps, the ratio will change to $7:9$. How many stamps are in both collections together?

Answer 1

Finding the total number of stamps:

Given,

The number of stamps in Alex’s collection is in ratio $3:5$ to the number of stamps in Freddy’s collection.

So,

Let the number of the stamps in Alex's collection be $3x$

The number of the stamps in Freddy's collection be $5x$

If Freddy gives Alex $10$ stamps to Alex, then

The number of the stamps in Alex's collection be $3x+10$

The number of the stamps in Freddy's collection be $5x-10$

Given, the ratio will change to $7:9$.

Therefore we can write,

$$\begin{gathered} \Rightarrow \frac{3x+10}{5x-10}=\frac{7}{9} \\ \Rightarrow 9\times \left(3x+10\right)=7\times \left(5x-10\right) \\ \Rightarrow 27x+90=35x-70 \\ \Rightarrow 70+90=35x-27x \\ \Rightarrow 160=8x \\ \Rightarrow x=\frac{160}{8} \\ \Rightarrow x=20 \end{gathered}$$

Therefore,

The number of stamps in Alex's collection is $3\times 20=60$

The number of stamps in Freddy's collection is $5\times 20=100$

The total number of stamps together they have is $80+100=160$

Hence, the total number of stamps in both collection together is $160$.