Respuesta :
Sells of a furniture store
Naming the variables
Let's say
C: number of chairs the store sells.
T: number of tables the store sells.
Writing the equations
We have two mathematical expressions in the description of the situation:
1. Every day, the store can ship a maximum of 39 pieces of furniture
This means that the number of chairs, C, and tables, T, sold must be less or equal than 39
C + T ≤ 39
2. The store sells chairs for $200 each and tables for $600 each and must sell at least $13000 worth of chairs and tables.
This is
the money they sell due to the chairs, is given by the product of the number of chars, C by the price of each:
$200 C
Similarly, the money they sell due to the tables is given by:
$600 T
Then, they sell
$200 C + $600 T
Since they must sell at least $13,000, then $200 C + $600 T must be higher than it:
$13,000 ≤ $200 C + $600 T
In conclusion, we have that:
C + T ≤ 39
$13,000 ≤ $200 C + $600 T
Finding the number of tables
We have that 20 chairs were sold: C=20.
Then, replacing in both expressions we have :
C + T ≤ 39
↓
20 + T ≤ 39
$13,000 ≤ $200 C + $600 T
↓
$13,000 ≤ $200 · 20 + $600 T
$13,000 ≤ $4,000 + $600 T
In the first expression, we have that:
20 + T ≤ 39
↓ taking 20 to the right side
T ≤ 39 - 20
T ≤ 19
Then, considering the first expression, the number of tables is 19 or less
In the second expression, we have that:
$13,000 ≤ $4,000 + $600 T
↓ taking $4,000 to the leftt side
$13,000 - $4,000 ≤ $600 T
$9,000 ≤ $600 T
↓ taking $600 to the leftt side
$9,000/$600 ≤ T
15 ≤ T
