the total number of cows and ducks on a farm is 35.All the cows have 74 more legs than all the ducks.How many cows are there on the farm?

Answer 1

D = Number of Ducks

C = Number of Cows

D + C = 35

C = 35 - D

Duck have 2 legs.

Cow have 4 legs

All the cows have 74 more legs than all the ducks.

This mean :

4 * C = 2 D + 74

4 * ( 35 - D ) = 2 D + 74

4 * 35 - 4 D = 2 D + 74

140 - 4 D = 2 D + 74 Subtract 74 to both sides

140 - 4 D - 74 = 2 D + 74 - 74

66 - 4 D = 2 D Add 4 D to both sides

66 - 4 D + 4 D = 2 D + 4 D

66 = 6 D Divide both sides by 6

66 / 6 = 6 D / 6

11 = D

D = 11

C = 35 - 11 = 24

Solution 24 Cows and 11 Ducks

Proof :

24 Cows have :

4 * 24 = 96 legs

11 Duck have :

11 * 2 = 22 legs

96 - 22 = 74