AAPL wrote:The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?

A. 3
B. 5
C. 10
D. 15
E. 21

The OA is D.

Local international ratio 5x/2x. Then local international ratio 5x/3x.

Can I say
$$\frac{5}{3}=\frac{5x}{2x+3}$$
and solve for x?

I don't have clear this PS question. I appreciate if any expert explains it to me. Thank you so much.

You could also back-solve and use a little logic. First, we know that local calls must be a multiple of 5, so only B, C, and D are options.
Next, we can see quickly that B doesn't make sense - if there had been exactly 5 local calls and 2 international calls, if 3 more international calls had been made, the ratio would have been 5:5, not 5:3. B is out.

Now we just have to test one of the two remaining answer choices. If it works, it's our answer. If it doesn't, the other is our answer.
If there had been 10 local calls, then there'd have been 4 international calls. (10:4 = 5:2.) If there'd been 3 more international calls, the ratio would have been 10:7. We want 5:3. So C is out.

We're left with D