Question

Each month, a shopkeeper spends 5x + 11 dollars on rent and electricity. If she spends 2x - 3 dollars on rent, how much does she spend on electricity? For which value(s) of x is the amount the shopkeeper spends on electricity less than $100? Explain how you found the value(s).

Answer 1

To find the amount the shopkeeper spends on electricity, subtract the amount spent on rent from the total monthly expenses. The amount the shopkeeper spends on electricity is 3x + 14 dollars. The amount spent on electricity is less than $100 for values of x that are less than 28.67.

Step-by-step explanation:

To determine how much the shopkeeper spends on electricity, we need to subtract the amount spent on rent from the total monthly expenses. The shopkeeper spends 5x + 11 dollars on rent and electricity each month and 2x - 3 dollars on rent. So, the amount spent on electricity can be found by subtracting the amount spent on rent from the total expenses:

Amount spent on electricity = Total expenses - Amount spent on rent

Amount spent on electricity = (5x + 11) - (2x - 3)

Amount spent on electricity = 5x + 11 - 2x + 3

Amount spent on electricity = 3x + 14

To find the values of x for which the amount spent on electricity is less than $100, we need to solve the inequality:

3x + 14 < 100

Subtracting 14 from both sides, we get:

3x < 86

Dividing both sides by 3, we get:

x < 28.67

So, the amount the shopkeeper spends on electricity is less than $100 for the values of x that are less than 28.67.