There are 12 birds in a flock. The ratio of seagulls to ducks is 1:2. How many seagulls must join the flock to change the ratio to 19:8?

Question

really stuck on this question need help with it asap

Answer 1

Ok, we know we have x seagulls and 2x ducks because they are in the ratio if 1:2.  We know the total number of birds is 12, therefore x plus 2x or 3x must equal 12. So set 3x = 12. Solving for x, x=4. So in the beginning we must have 4 seagulls and 8 ducks. To get to the end ratio of 19:8 we already have the correct number of ducks. We need 19 seagulls and we currently have 4, so we need 15 more Seagulls.

Answer 2

Number of seagulls in the flock now = 1/3 * 12 = 4 seagulls

Number of ducks -= 12 - 4 = 8 ducks

Let x be the new seagulls that should join the flock to make the ratio change to 19:8

Total number of birds = x+12

Total number of seagulls = x+4 , since all the birds that are joining are seagulls

Therefore the equation can be written as

19/(19+8) * (x+12)  = (x+4)

19(x+12) = 27(x+4)

8x = 120

x = 15

Number of seagulls that should join the flock = 15

Check:

Total # of seagulls = 4+15 = 19

Number of ducks = 8 ( This is not changing)

New Ratio = 19:8