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.
The solution manual is referring to the wrong problem which is related to money.
Here is how to solve. This does not match up exactly with this chapter but should have been 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
So r = 30-h
Now substitute this into the second to get
86 = 2h + 4r
86 = 2h + 4(30-h) = 2h + 120 – 4h = -2h +120
So now 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.
From: June <PrincessJune@protonmail.com>
Reply-To: June <PrincessJune@protonmail.com>
Date: Saturday, July 27, 2019 at 3:34 PM
To: Dale Callahan <firstname.lastname@example.org>
Subject: Re: A question on Algebra
I have two questions from Elementary Algebra.
In Chapter 16, Lesson 2, Set I, Question #3 and in Chapter 17, Lesson 2, Set II, Question #12, their respective answers don’t seem to match up with the questions. Is this a mistake? And if not, could you please explain how to obtain the correct answers?
Thank you very much.
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