Anna is an avid reader. her generous grandparents gave her money for her birthday, and she decided to spend at most $150.00 on books. reading spot is running a special: all paperback books are $8.00 and hardback books are $12.00. anna wants to purchase at least 12 books.

1.) write a system of inequalities to reach po represent the situation.

2.) graph the region of the solutions to the inequality.

3.) name two different solutions for anna's situation.

1) equations 1, 2, 3  and 4

2)  see picture attached (the region of the solutions is in yellow)

3) x = 18.75 and y =0

   y = 12.5 and x =0

Step-by-step explanation:

Let's call x the number of paperback books bought and y the number of  hardback books bought.

She decided to spend at most $150.00. All paperback books are $8.00 and all hardback books are $12.00. Combining this information we get:

x*8 + y*12 ≤ 150 (eq.  1)

Anna wants to purchase at least 12 books. Mathematically:

x + y ≥ 12 (eq. 2)

On the other hand,  both the number of paperback books bought and the number of  hardback books bought must be positive, that is:

x ≥ 0 (eq. 3)

y ≥ 0 (eq. 4)

3) One possible solution is got if we make y = 0 and to take eq. 1 as an equality, then:

From eq. 1: x*8 = 150

x = 150/8 = 18.75

equations 2 and 3 are also satisfied

Another option is to make x = 0 and to take eq. 1 as an equality, then:

From eq. 1: y*12 = 150

y = 150/12 = 12.5

equations 2 and 4 are also satisfied

In order to do this problem, you have to divide 16 by 2 to see how many times x was multiplied. you would find that x was multiplied 8 times, so in order to find y, you would multiply 3.5 eight times.

y = 28 when x = 16