Farmer Bob of the Martian Colony counted his sheep and chickens in an unusual way. When he finished, he reported that he had counted 86 feet and 26 heads. Use a guess and check table to find how many sheep and chickens are owned by the famer.
I have two solutions for you.
I am going to imagine "constructing" sheep and chickens from marshmallows and toothpicks. A marshmallow with two toothpicks in it is a chicken
You have 26 heads (marshmallows) and 86 feet (toothpicks). Put 2 toothpicks into each marshmallow to make 26 chickens. You have 86 - 2x26 = 34 toothpicks remaining, that is 17 pairs of toothpicks remaining. Put these 17 pairs of toothpicks into 17 of the "chickens" to turn them into "sheep". Now you have 17 sheep and 26 - 17 = 9 chickens. [Check: 17 + 9 = 26 heads and 4x17 + 2x9 = 86 feet.]Penny
Lets now try 11 sheep. This means 15 chickens. The number of feet is
Lets now try 12 sheep. This means 14 chickens. The number of feet is
Have you noticed a pattern? The number of feet is going up by 2 for each sheep we add. To get from 76 to 86 feet, we need to go by 2 five more times. This suggests that we try 12+5=17 sheep. With 17 sheep, there are 9 chickens, and the number of feet is 17x4+9x2=86. Therefore, there are 17 sheep and 9 chickens. Paul