Question

Michael is an avid reader, his generous grandparents gave him money for his birthday, and he decided to spend at most $150 on books. Barnes and Noble is running a special: all paperback books are $8.00 and hard back books are $12.00. Michael wants to purchase at least 12 books.

Write a system of inequalities to represent the situation.

Answer 1

The system of inequality to represent the situation is

p + h
`\geq` 12

8 p + 12 h = 150

Explanation:

Given as :

Total money to be spend on books = $150

The cost of each paperback book = $8

The cost of each hard back book = $12

The total number of books to be purchased = 12

Let The number of paperback books = p

Let The number of hard back books = h

According to question

Total number of books to be purchased = number of paperback book + number of hard back book

i.e p + h
`\geq` 12 ...........A

Again

Total money to be spend on books = number of paperback books × cost of each paperback book + number of hard back books × cost of each hard back book

i.e p × $8 + h × $12 = $150

Or, 8 p + 12 h = 150 .........B

So, The system of inequality to represent the situation =

p + h
`\geq` 12 and 8 p + 12 h = 150

Hence, The system of inequality to represent the situation is

p + h
`\geq` 12 and 8 p + 12 h = 150 . Answer