Question

1) A farm has chickens and cows. You ask the farmer how many chickens he has, and how many cows he has. The farmer tells you he has 28 healthy animals, and they have a total of 64 legs. How many of his animals are cows?

2) Andrew has a collection of soda bottles. Some of them are 12-ounce bottles, and others are 16-ounce bottles. If the collection contains 20 bottles which hold a combined 300 ounces, how many of the soda bottles are 12-ounce bottles?

Need two variables and two equations for each. It also needs to be solved.

Answer 1

1. c=cows b=chicens c+b=28 chicen has 2 legs cow has 4 legs 4c+2b=64 c+b=28 4c+2b=64 multiply first equaiton by -2 and add to second -2c-2b=-56 4c+2b=64 + 2c+0b=8 2c=8 divide 2 c=4 sub c+b=28 4+b=28 minus 4 b=24 4 cows and 24 chicens 2. t=twelve oz s=sixteen oz t+s=20 12t+16s=300 find t multiply first equation by -16 -16t-16s=-320 add to first equation -16t-16s=-320 12t+16s=300 + -4t+0s=-20 -4t=-20 divide -4 t=5 five 12 oz bottles 1. 4 cows, 24 chicen 2. 5 twelve oz bottles