Word Problem Equation Help #2

[Cindy Burgess]

You have a gift certificate to a book store worth $90. Each paperback book is $7 and each hardcover book is $13. You must spend at least $20 in order to use the gift certificate. Let x=the number of paperback books and y=the number of hardback books. 1. Write a system of inequalities to model the number of each kind of book you can buy----Does it look like this? 7x+13y is greater than or equal to 20 and 7x+13y is less than or equal to 90 2. graph the system below 3. state a possible solution I'm not sure if 1 is right. If it is 13y>or = to -7x+20 y>= to -7/13x + 20/13 Using y=mx+B Now, I'm totally lost! PLEASE HELP

 

[stapel]

As currently formatted, your post is difficult for me to read, so I've reformatted a bit:

You have a gift certificate to a book store worth $90. Each paperback book is $7 and each hardcover book is $13. You must spend at least $20 in order to use the gift certificate.

Let "x" stand for the number of paperback books and "y" stand for the number of hardback books.

1. Write a system of inequalities to model the number of each kind of book you can buy
2. Graph the system below.
3. State a possible solution.

My work:
1. Does it look like this?
. . . .7x + 13y >= 20
. . . .7x + 13y <= 90

2. (Can't show this.)

3. I'm not sure if 1 is right. If it is, then part of the solution, I think, is:

. . . .13y >= -7x + 20
. . . .y >= to -(7/13)x + 20/13 (this is using "y = mx + b" form)

Now, I'm totally lost! PLEASE HELP

1) Your system of equations looks good to me. But you might also want to include that the variables can't be negative.

2) Your graph should have a band of solutions, kind of like is shown in this image (but with different intercepts, etc, of course).

3) For a system of linear inequalities, "the" solution is the set of all single-point solutions; in this case, "the" solution is that band. But they only asked for "a" solution, and any point in "the" solution will be "a" solution.

Mathematically.

Technically, in terms of this exercise, since you can't buy portions of books, solutions will only be the whole-number points in "the" solution. So pick any one of those.

 

[HallsofIvy]

You have a gift certificate to a book store worth $90. Each paperback book is $7 and each hardcover book is $13. You must spend at least $20 in order to use the gift certificate. Let x=the number of paperback books and y=the number of hardback books. 1. Write a system of inequalities to model the number of each kind of book you can buy----Does it look like this? 7x+13y is greater than or equal to 20 and 7x+13y is less than or equal to 90
In other words, \(\displaystyle 20\le 7x+ 13y\le 90\)

2. graph the system below

The lines \(\displaystyle 7x+ 13= 20\) and \(\displaystyle 7x+ 13y= 90\) form the boundaries of the region

3. state a possible solution I'm not sure if 1 is right. If it is 13y>or = to -7x+20 y>= to -7/13x + 20/13 Using y=mx+B Now, I'm totally lost! PLEASE HELP

Do you know what "possible solution" means? Find specific values of x and y so that 7x+ 13y is between 2- and 90. There are an infinite number of (x, y) pairs that satisfy that- choose one.