An online furniture store sells chairs for $150 each and tables for $350 each. every day, the store can ship a maximum of 20 pieces of furniture and must sell at least $4800 worth of chairs and tables. if 18 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.

The solution is not possible for the number of chair to be sold 18 , It is only possible if the number of chair to be sold is 11 and the number of tables to be sold is 9  .

Step-by-step explanation:

Given as :

The cost of each chairs = $ 150

The cost of each tables = $ 350

The maximum number of chair and table can ship = 20

The minimum selling amount of chairs and tables = $ 4800

Let The number of chair to be ship = C

And The number of table to be ship = T

So , According to question

C + T = 20         .......1

And $ 150 × C + $ 350 × T = $ 4800         ....2

So, From first eq

$ 150 × ( C + T ) = $ 150 × 20

Or, $ 150 C + $ 150 T = $ 3000

So, Solving eq

( $ 150 × C + $ 350 × T ) - ( $ 150 C + $ 150 T ) = $ 4800 - $ 3000

Or, ( $ 150 C - $ 150 C ) ( $ 350 T - $ 150 T ) = $ 1800

Or, 0 + $ 200 T = $ 1800

Or,  T =

∴  Number of Tables T = 9

So, Number of chairs C = 20 - T = 20 - 9 = 11

Thus to meet the requirement The number of Tables to be sold = 9 and the number of chairs to be sold = 11

But , If the number of chair to be sold = 18

And Since The maximum of pieces of furniture to be sell = 20

So, The number of tables to be sold = T = 20 - 18 = 2

∴ For table T = 2 And chair C = 18

Let check the net worth

I.e ( $ 150 × C + $ 350 × T )

Or, ( $ 150 × 18 + $ 350 × 2 )

Or, $ 2700 + $ 700 = $ 3400

But The company must sell the furniture of net worth at least $ 4800 ,  So this is not possible to sell 18 chair .

Hence The solution is not possible for the number of chair to be sold 18 , It is only possible if the number of chair to be sold is 11 and the number of tables to be sold is 9  . Answer

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x