Question

system of inequalities word problems
score: 0/1 penalty: 1 off
question
an online furniture store sells chairs for $200 each and tables for $600 each. every day, the store can ship a maximum of 23 pieces of furniture and must sell at least $7400 worth of chairs and tables. if 10 chairs were sold, determine the minimum number of tables that the store must sell in order to meet the requirements.
answer attempt 1 out of 2
additional solution no solution

Explanation:

Step1: Define variables and constraints

Let \( c \) be the number of chairs and \( t \) be the number of tables. We know \( c = 10 \). The shipping constraint: \( c + t \leq 23 \), so \( 10 + t \leq 23 \) (but we also have the revenue constraint: \( 200c + 600t \geq 7400 \)). Substitute \( c = 10 \) into the revenue inequality: \( 200(10) + 600t \geq 7400 \).

Step2: Solve the revenue inequality

Calculate \( 200(10) = 2000 \). So the inequality becomes \( 2000 + 600t \geq 7400 \). Subtract 2000 from both sides: \( 600t \geq 7400 - 2000 = 5400 \). Then divide both sides by 600: \( t \geq \frac{5400}{600} = 9 \). Now check the shipping constraint: \( 10 + t \leq 23 \implies t \leq 13 \). Since 9 is within \( t \leq 13 \), the minimum \( t \) is 9.

Answer:

9