Question

Christina's house sits for her neighbors. She charges $35 if she stays overnight and $20 if she just checks on the house. She wants to make at least $150. So far she has stayed overnight at 2 houses. Which equation/inequality below describes the number of houses she has to check to reach her goal?

a) 2($35) + $20x = $150
b) 2($20) + $35x = $150
c) $35 + $20x ≥ $150
d) $20 + $35x ≥ $150

Answer 1

The correct inequality to represent the number of houses Christina needs to check to reach her goal is 2($35) + $20x ≥ $150, which accounts for the two overnight stays she has already completed and the additional houses she needs to check at $20 each to make at least $150.

Step-by-step explanation:

The question asks for the equation or inequality that represents the number of houses Christina needs to check on to reach her goal of at least $150, given that she charges $35 for an overnight stay and has already stayed at 2 houses. We know that she has made 2($35) from the overnight stays. Let's define x as the number of houses she needs to check on, each at $20. To find out how many more houses she needs to check on, we have to add $20x to the fixed amount she has earned from the overnight stays. We can set up an inequality because she wants to make at least $150, so she could make $150 or more.

The correct equation/inequality is 2($35) + $20x ≥ $150. This translates to:

$70 + $20x ≥ $150

Therefore, Christina has to check enough houses to ensure that the total amount from the house checks and overnight stays is at least $150.