Question

An online furniture store sells chairs for $100 each and tables for $550 each. Every day, the store can ship at most 21 pieces of furniture and must sell no less than $5700 worth of chairs and tables. If 10 chairs were sold, determine the minimum number of tables that the the store must sell in order to meet the requirements. If there are no possible solutions, submit an empty answer.

Answer 1

Answer:{ 9, 10, 11 }

Explanation:

Answer 2

9 tables

Explanation:

Let x be the number of chairs sold and y be the number of tables sold.

Chairs are sold for $100 each, then x chairs cost $100x.

Tables are sold for $550 each, then y tables cost $550y.

Every day, the store can ship at most 21 pieces of furniture, then

`x+y\le 21`

Store must sell no less than $5,700 worth of chairs and tables, then

`100x+550y\ge 5,700`

If 10 chairs were sold, then
`x=10.` Substitute this value into both inequalities:

1.
`10+y\le 21\Rightarrow y\le 11`

2.
`100\cdot 10+550y\ge 5,700\Rightarrow 550y\ge 4,700\Rightarrow y\ge (470)/(55)=8(6)/(11)`

Hence,
`8(6)/(11)\le y\le 11`

The minimum number of tables that the the store must sell in order to meet the requirements is 9 tables