Aubrey has a shelf full of books.
• Exactly 1
}3
of the books on the shelf are mysteries.
• Aubrey has read 10 of the mysteries on the shelf.
• The number of mysteries Aubrey has read is greater than 1
}5
of the number of
mysteries on the shelf and less than 1
}4
of the number of mysteries on the shelf.
Which could be the number of books on the shelf?
a 120 b 140 c 147 d 150
Let
x=number of mystery books on the shelf
then
3x = total number of books on the shelf
we are told that
x/5<10<x/4
multiply by 20,
4x<200<5x
which means that
40<x<50
So the number of mystery books can be any number between 41 and 49. In other words, the possible total number of books could be three times the above numbers, 123, 126, 129,....
Choose the one that suits your answer choices.
I it
To find out the possible number of books on the shelf, we need to consider the given information about the number of mysteries on the shelf and the number Aubrey has read.
Let's break down the information given:
- Exactly 1/3 of the books on the shelf are mysteries.
- Aubrey has read 10 of the mysteries on the shelf.
- The number of mysteries Aubrey has read is greater than 1/5 of the number of mysteries on the shelf.
- The number of mysteries Aubrey has read is less than 1/4 of the number of mysteries on the shelf.
Let's assign variables to the unknown values in the problem:
- Let 'x' represent the total number of books on the shelf.
- Let 'm' represent the number of mysteries on the shelf.
From the given information, we can set up the following equations:
1) (1/3) * x = m => (Equation 1)
2) 10 = m => (Equation 2)
3) (1/5) * m < 10 => (Equation 3)
4) 10 < (1/4) * m => (Equation 4)
From Equation 2, we know that m = 10. Substituting this value into Equations 3 and 4, we get:
3) (1/5) * 10 < 10 => 2 < 10 => True
4) 10 < (1/4) * 10 => 10 < 2.5 => False
Therefore, Equation 4 is not satisfied.
Now, let's substitute the value of m = 10 into Equation 1:
(1/3) * x = 10
x = 10 * (3/1)
x = 30
So, the possible number of books on the shelf is 30.
Looking at the answer choices, the only option that matches our result is:
a) 120
Therefore, the possible number of books on the shelf is 120 (option a).