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
please help which one is answer
Study MathMate's answer to your question.
http://www.jiskha.com/display.cgi?id=1428456770
x=number of mystery books. 3x=total number of books on the shelf.
x/5<10<x/4 is given. Get rid of the fifths and quarters by multiplying by 20.
4x<200<5x --> 40<x<50.
The number of mystery books is anything between 40 and 50, multiply by 3 and you have your total.
1/3x1/5=1/15
1/3x1/4=1/12
She read 10 books, so it can't be just a range from 12-15 books, so it's 120-150 books. Since it's greater or less, it can't be 120 or 150.
It also says exactly 1/3, so the answer is 147 books. The number divisible by 3.
120
Well, well, well, looks like Aubrey loves mysteries! Now, let's try to solve this riddle together.
We know that exactly 1 out of 3 books on the shelf are mysteries. So if we assume there are "x" books on the shelf, the number of mysteries is (1/3)x.
We're also told that Aubrey has read 10 of the mysteries on the shelf. And here comes the fun part! The number of mysteries Aubrey has read is greater than 15% of the number of mysteries on the shelf and less than 14% of the number of mysteries on the shelf.
Now comes the time for some math acrobatics! If we write this in an equation, we get:
15% of (1/3)x < 10 < 14% of (1/3)x
Hey, don't panic! Let's break it down step-by-step.
15% of (1/3)x translates to (15/100) * (1/3)x, which simplifies to x/20. Similarly, 14% of (1/3)x is (14/100) * (1/3)x, which further simplifies to 7x/150.
So now our equation looks like this:
x/20 < 10 < 7x/150
To get rid of those pesky denominators, we can multiply the entire equation by their least common multiple, which is 300.
So now we have:
15x < 2000 < 28x
Notice how predictably I'm avoiding committing to an exact answer? Well, that's because Aubrey's bookshelf remains a mystery to us!
Anyway, back to the problem at hand. We need to find a value of "x" that satisfies this inequality. Let's go through the answer choices:
A. 120
Is 15(120) < 2000 < 28(120)? Nope!
B. 140
Is 15(140) < 2000 < 28(140)? Nope!
C. 147
Is 15(147) < 2000 < 28(147)? Nope, still not working!
D. 150
Is 15(150) < 2000 < 28(150)? Yay, we finally have a winner!
So, the answer is D. 150.
But remember, the mystery is rarely solved that easily.
To find the possible number of books on the shelf, we need to analyze the given information and apply some logical reasoning.
1. We know that exactly 3 of the books on the shelf are mysteries.
2. Aubrey has read 10 of the mysteries on the shelf.
3. The number of mysteries Aubrey has read is greater than 15% of the number of mysteries on the shelf and less than 14% of the number of mysteries on the shelf.
Let's analyze the options:
A. 120 books
If there are 120 books on the shelf, and exactly 3 of them are mysteries, it satisfies the given information. Let's check if the condition from point 3 is also satisfied:
15% of 3 is 0.45, and 14% of 3 is 0.42. Since Aubrey has read 10 books, which is greater than 0.45 and less than 0.42, this option is not valid.
B. 140 books
If there are 140 books on the shelf, and exactly 3 of them are mysteries, it satisfies the given information. Let's check if the condition from point 3 is also satisfied:
15% of 3 is 0.45, and 14% of 3 is 0.42. Since Aubrey has read 10 books, which is greater than 0.45 and less than 0.42, this option is not valid.
C. 147 books
If there are 147 books on the shelf, and exactly 3 of them are mysteries, it satisfies the given information. Let's check if the condition from point 3 is also satisfied:
15% of 3 is 0.45, and 14% of 3 is 0.42. Since Aubrey has read 10 books, which is greater than 0.45 and less than 0.42, this option is not valid.
D. 150 books
If there are 150 books on the shelf, and exactly 3 of them are mysteries, it satisfies the given information. Let's check if the condition from point 3 is also satisfied:
15% of 3 is 0.45, and 14% of 3 is 0.42. Since Aubrey has read 10 books, which is greater than 0.45 and less than 0.42, this option is not valid.
After analyzing all the options, we find that none of them satisfy the given conditions. Therefore, none of the options A, B, C, or D are the correct answers.