This is an error in the book by Master Books (ISBN: 978-0890519851) – the book with the blue cover showing the world.
The problem is discussing hens and rabbits with a total of 30 heads and 86 feet.
ERROR: The solution manual is referring to the wrong problem which is related to money.
Here is how to solve. Simultaneous equations are covered in Chapter 7. So if you forget how to solve these, refer back to chapter 7.
heads = # hens + # rabbits
feet = 2 x # hens + 4x number of rabbits
So let h be the number of hens and r be the number of rabbits.
We can re-write the above as
heads = 30 = h + r
feet = 86 = 2h + 4r
30=h+r
So r = 30-h
Substitute this equation into the second equation to get
86 = 2h + 4r
86 = 2h + 4(30-h) = 2h + 120 – 4h = -2h +120
Rearrange to get
2h = 120-86 = 34
h = 17 (number of hens)
Now we can find the rabbits are
R = 30-h = 30-17 = 13
Checking our work
13 + 17 = 30 (total number of heads)
2 x 17 + 4 x 13 = 86 which are the number of feet.
Correct!
