Help...algebra word problem?

Question

Problem: Last year, Kirsten read one fourth as many biographies as mysteries and eighteen more science fiction books than biographies. The number of Nature books that she read was one less than the difference between the number of mysteries and the number of biographies. If Kirsten read four times as many science fiction books as Nature books, how many books did she read in all?

x= number of mystery book read

Answer 1

B = # of biographies
M = # of mysteries
S = # of science fiction
N = # of nature books

one fourth as many biographies as mysteries

1) B = M/4

eighteen more science fiction books than biographies

2) S = B + 18

number of Nature books that she read was one less than the difference between the number of mysteries and the number of biographies

3) N = M - B - 1

read four times as many science fiction books as Nature books,

4) S = 4N

She read B + S + N + M books

Solve eq 1 for M, substitute into eq 3

3) N = 4B - B - 1
3a) N = 3B - 1

Substitute this into eq 4

4) S = 4(3B - 1) = 12B - 4

Set this = to eq 2

12B - 4 = B + 18
11B = 22
B = 2

2) S = 2 + 18 = 20

3a) N = 3(2) - 1 = 6 - 1 = 5

Solve eq 3 for M

3b) M = N + B + 1
M = 5 + 2 + 1 = 8

B + S + N + M = 2 + 20 + 5 + 8 = 35

Answer 2

She read 2 Biographies, 8 Mysteries, 20 Science Fiction Books, and 5 Nature Books. You just start out with the first object mentioned, the biographies, and assign that the value of 1. she read one fourth as many biographies as mysteries, that means that the number of mysteries is four times that of the number of biographies. so if bio = 1 then mysteries =4. then you add 18 to 1 for the science fiction books and the scifi books = 19. the number of nature books is one less than the difference between the mysteries and biographies. in this case the difference is 3 so one less would be 2. so we have nature books =2. but that's not right, according to the last line (scifi books = 4xNature books), because 4x2=8. so we increase the smallest number, the biographies, to 2. that increases mysteries to 8, raises scifi books to 20, and raises nature books to 5. 4x5=20. it all balances out.

Answer 3

Let B = Biographies
Let S = Sci Fi
Let N = Nature
Let M = Mysteries

Determine the Given equaitions:
1) 4B = M
2) S -18 = B
3) N +1 = M - 8
4) S = 4N

Hint: Double check each of the given equations to make sure you have them correct. Plug in easy numbers and see if it is true. E.g. To check on equation 1) above you could say that possibly there were 12 mysteries read, that would mean there should be 3 biographies read. Plug in 12 and 3 into equaition one and just double check that you have it correct. Do this on every sentence and given equation. Simply plug in easy examples to check that your work is correct.

TO SOLVE:
start reducing to a single variable so that you can determine one variable. I will solve for N.

Replace B in 3):
N + 1 = M - (S - 18)

Replace M in above
N + 1 = 4B - (S - 18)

Replace B in above
N + 1 = 4(S -18) - (S - 18)

Reduce this a little so it is easier to work with:
N + 1 = 4S - 72 - S + 18
N + 1 = 3S - 54
N = 3S - 55

Now Replace S with equation 4) from Given:
N = 3(4N) - 55

Solve for N
N = 12N - 55
-11N = -55
N = 5 [first part of solution!]

Now it gets easy. Determine the other variables using the given equations.

Use 4) S = 4(5) = 20
S = 20

USe 2) to solve for B:
20-18 = B
B = 2

Use 1) to solve for M
4(2) = M
M = 8

Now take N, S, B, M, and plug them into the given equations to make sure they all work properly.
E.g. using 3)
N + 1 = M - B
5 + 1 = 8 - 2
6 = 6 (so it is working)

Check all of them this way to make sure they ALL work.


To get the Final Answer and the Total # of Books:
add them all together
N + S + B + M = Total
5 + 20 + 2 + 8 = 35

Answer 4

what you need to do is set up each relationship, for example she read a fourth as many biographies as mysteries, so
b=(1/4)*m, which says the number of biographies she read is a fourth the numbe of mysteries
s=b+18 (she read 18 more sci-fi than she did biography)
n=(m-b)-1 (she read one less nature book than the difference of mystery and biography)
s=4*n (4 times as many sci-fi as nature books)
Total number of books she read=b+m+s+n
b=(1/4)*m, m=4b
s=b+18
n=(m-b)-1, substitute 4b for m to get n=3b-1
s=4*n, substitute b+18 for s and 3b-1 for n to get
b+18=4*(3b-1)
b+18=12b-4
22=11b
b=2
m=4b=2*2=8
s=b+18=2+18=20
n=3b-1=3*2-1=5
total books = b+m+s+n=2+8+20+5=35

Answer 5

b = biographies
m = mysteries
s = science fiction
n = nature
T = total = b + m + s + n

4b = m
s - 18 = b
n +1 = m - b
4n = s

n + 1 = 3b
4n - 18 = b
n + 1 = 3(4n - 18)
n + 1 = 12n - 54
55 = 11n
n = 5
s = 4n = 20
5 + 1 = 3b; b = 2
m = 4b = 8
T = 5 + 20 + 2 + 8 = 35

Answer 6

b stands for biographies
n stands for nature books
s stands for science fiction books
m stands for mystery books

she rea one furth as many bios as myteries. she read more mysteries. 4xb=m.
she read MORE sifi than bios so
b+18=s
differecen between mys and bios is m-b
one less than this diff is m-b-1
thats what nature books equal...one less than that diff.
n=m-b-1
she read more sifi than natures so
s=4xn
now subtract two eaquations to eliminate s
-s=-4n
s=b+18
-------------------
0=b-4n+18 so 4n=b+18
now add some others together
4n=b+18
but 4b=m so b= .25m
4n= .25m + 18