Question

A bird shooter was asked how many birds he had in his bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds did he have in all in his bag?

A. 9

B. 18

C. 27

D. 36

Answer 1

If possible, assign a variable to the value the problem asks you to find. Let's use: T = total number of birds.

Also, let S = number of sparrows
P = number of pigeons
D = number of ducks

Translate:
"all sparrows but six" means S = T - 6
"all pigeons but six" means P = T - 6
"all ducks but six" means D = T - 6
Also,
S + P + D = T (the total number of birds in the bag)

Now, the math:
S = T - 6
P = T - 6
D = T - 6
--------------- (add the three equations)
S+P+D = 3T - 18
T = 3T - 18 (substitute T for S+P+D)
T + 18 = 3T (add 18 to both sides)
18 = 2T (subtract T from both sides)
9 = T [There were nine birds in the bag]

Check:
3 sparrows (this is all but 6)
3 pigeons (this is all but 6)
3 ducks (this is all but 6)
Total 9 birds in the bag.