Question

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.

Answer 1

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

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

Answer 2

The solutions for 3 questions are explained one after the other below.

Explanation:

1).Let x be the number of paperback books that she buys, y be the number of hardback books that she buys.

for the first condition, i.e, she has decided to spend at most $150.00 on books,the required inequality will be :

`8x+12y\leq 150`

for the second condition , i.e, she wants to purchase at least 12 books,

the required inequality will be:

`x+y\geq 12`

2). the graph is in the attachment..

3). x,y are the two required solutions. where,

x =number of paperback books she buys.

y=number of hardback books she buys.