Question

There were 420 birds migrating to the south in the sky this morning.  If the ratio of godwits to geese in the sky this morning was 20:40, how many more geese were in the sky?

Answer 1

We know that the total was 420 birds. 

We also know that the ratio of Godwits geese was 20:40, so 2: 4, which after shortening is 1: 2. Now we know that geese is twice the Godwits. 

Arrange the relationship:

x + 2x = 420
3x = 420 |:3
x = 140
2x = 2 * 140 = 280

We see that the geese is 280, and 140 Godwits. In total 420.

Answer 2

Total number of birds = 420

Godwits / Geese  =  20 : 40   = 20 /40  = 1 / 2      (40 = 20 * 2 , cancel  20 on numerator and denominator)

 2   Godwits =   1 Geese      by cross multiplying on both sides

Godwits + Geese = 420
substitute in place of geese 2 Godwits
Godwits + 2 Godwits = 420
3 godwits = 420
godwits = 420 / 3    =    140 * 3 / 3  = 140
geese = 2 * godwits = 2 * 140  =  280