Question
A tour director is hiring boats to transport a group of tourists across a river. He must make sure there is room for at least 38 passengers, the number of tourists in the group. A dinghy can seat 6 passengers and a flatboat can seat 1 passenger.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of dinghies
y = the number of flatboats
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of dinghies
y = the number of flatboats
Answers
GPT-4o mini
To describe the situation, we need to formulate an inequality based on the seating capacity of the boats and the requirement to accommodate at least 38 passengers.
Given:
- Each dinghy can seat 6 passengers, so the total seating from dinghies is \(6x\).
- Each flatboat can seat 1 passenger, so the total seating from flatboats is \(1y\) (or simply \(y\)).
The total seating capacity must be at least 38. Therefore, we can express this requirement with the following inequality:
\[
6x + y \geq 38
\]
To write this in standard form, we can rearrange it:
\[
6x + y - 38 \geq 0
\]
Thus, the inequality in standard form is:
\[
6x + y - 38 \geq 0
\]
This represents the situation where the resources (boats) must account for a minimum of 38 passengers.
Given:
- Each dinghy can seat 6 passengers, so the total seating from dinghies is \(6x\).
- Each flatboat can seat 1 passenger, so the total seating from flatboats is \(1y\) (or simply \(y\)).
The total seating capacity must be at least 38. Therefore, we can express this requirement with the following inequality:
\[
6x + y \geq 38
\]
To write this in standard form, we can rearrange it:
\[
6x + y - 38 \geq 0
\]
Thus, the inequality in standard form is:
\[
6x + y - 38 \geq 0
\]
This represents the situation where the resources (boats) must account for a minimum of 38 passengers.