Question

Help me please

Ms. Garcia wants to buy some books for her classroom. Adventure books cost $8 each and mystery books cost $12 each. Ms.Garcia wants to buy at least 8 books but she needs to spend less than $120. What is the maximum number of mystery books that she can buy?

Answer 1

10 mystery books

Answer 2

Why ?
How do you know ?

Answer 3

simple math 12*8 gives you 96 so then 96+24= 120 thus 10 books

Answer 4

to 96 yo can buy 24$ worth of bools

Answer 5

*you

Answer 6

I don't get it... Is that the maximum?

Answer 7

what are your answers

Answer 8

what do you mean?

Answer 9

what answers do you have for the problem

Answer 10

None

Answer 11

can you only type numbers

Answer 12

???

Answer 13

Dan, I'll gladly help you, but I'm currently committed to helping another person with a different problem. If you can afford to wait 5 min. or so, please do. MM

Answer 14

Ok thanks... I'll be waiting

Answer 15

Thanks for your patience. I still have that other student waiting, but I'm going to get you started on the solution of this problem.

Answer 16

Thanks

Answer 17

Daniel (or is it Dan?),
let a=number of adventure books purchased
let m = number of mysteries purchased
This dear lady wants to buy at least 8 books, right?

Therefore, we set up the inequality a + m (equal to or greater than) 8.

Answer 18

how mch sense does this make to you, Dan?

Answer 19

I got that

Answer 20

Now our lovely customer doesn';t want to spend more than $120.

Therefore, the total she spends on all her purchased books must be <= $120.

Everything in this inequality must be in dollars.

So...

Answer 21

suppose she buys a adventure books, and that each adventure book costs $8.

Here's what I'd write for the amount she spends on adventure books:

a books
----------
$8/a book

Answer 22

Something's not quite right here, but perhaps you yourself could fix it.

If the lady buys the quantity a of adventure books and each adventure book costs $8, then how much does she spend on adventure books, as a function of a?

Answer 23

any clue yet?

Answer 24

Nop.. Just guessing 1/8 ?

Answer 25

Or 1/8a something like that????

Answer 26

How about

a books
------------ = $8a total for the a adventure books. Make sense?
1 book/$8

Then, for the mystery books,

m books
------------ = $12m total for the m mysteries
1 book/$12

Then we end up with 2 equations in 2 unknowns:

Answer 27

a+m=> 12
$8a + $12b <= $120

Know how to solve this system of linear inequalities?

Please think about this for a moment; I'll be back in a min. or two.
do as much as you can.

Answer 28

Ok

Answer 29

Hey, Dan,

Have you graphed inequalities before?

with x+y => 8,

Just graph the line x+y=8 and SHADE the area ABOVE the line. Sound at all familiar?

Answer 30

yes

Answer 31

I urge you to try graphing these two inequalities.

Use the Draw utility if possible.

the line a+m=> 12 has vertical intercept (0,8) and horiz intercept (8,0).
the other line, 8a + 12 m <= 120 has vert. int. (0,15) and horiz intercept (10,0).

Hope this helps. Do all you can. I'll be back!