Anna is an avid reader. Her generous grandparents gave her money for her birthday, and she decided to spend at most $150.00 on b
ooks. 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.) 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.
2 answers:
Answer:
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
Answer:
The solutions for 3 questions are explained one after the other below.
Step-by-step 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 :
for the second condition , i.e, she wants to purchase at least 12 books,
the required inequality will be:
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.
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