SOLUTION: A group of goats and ducks have a total of 99 heads and legs among them. There are twice as many ducks as there are goats. How many are there of each?

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: A group of goats and ducks have a total of 99 heads and legs among them. There are twice as many ducks as there are goats. How many are there of each?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 114865This question is from textbook Harcourt Math
: A group of goats and ducks have a total of 99 heads and legs among them. There are twice as many ducks as there are goats. How many are there of each? This question is from textbook Harcourt Math

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
g = number of goats
d = number of ducks
Each goat has 1 head and 4 legs, so there are 5g heads and legs supplied by the goats.
Each duck has 1 head and 2 legs, so there are 3d heads and legs supplied by the ducks

5g%2B3d=99,

We also know that there are twice as many ducks as goats, so d=2g

Substituting:
5g%2B3%282g%29=99,
11g=99
g=9, so there are 9 goats. This means that there are d=2%2A9=18 ducks.

Check:
9 goat heads
4 * 9 = 36 goat legs
18 duck heads
2 * 18 = 36 duck legs
9 + 36 + 18 + 36 = 99, Check!