Members of a community center are planning a field trip to the zoo. More than 50 people will go on the trip. Ten people are providing their own transportation. The rest of the people will ride in k vans. Each van can carry 5 people.
Which inequality can be used to represent the situation?
Responses
5(k+10)>50
5 left parenthesis k plus 10 right parenthesis greater than 50, ,
5k+10>50
5 k plus 10 greater than 50
k+15>50
k plus 15 greater than 50, ,
k−15>50
k plus 10 greater than 50
The correct inequality that represents the situation is: 5(k+10)>50.
The inequality that can be used to represent the situation is 5(k + 10) > 50.
To understand why, we need to break down the information given in the question. First, we know that there will be more than 50 people going on the trip. So, we can represent the total number of people as "50 + (number of people in vans)."
Next, we are told that 10 people are providing their own transportation, which means they won't be riding in the vans. The remaining number of people riding in the vans would be represented as "(number of people in vans) = total people - 10."
Finally, we are informed that each van can carry 5 people. So, we can calculate the maximum number of people in the vans by dividing the total number of van seats by 5: "(number of vans) x 5."
Combining all this information, we get the inequality:
(number of people in vans) = total people - 10 > 50
(number of people in vans) > 40
(number of vans) x 5 > 40
k > 8
Hence, the inequality that represents the situation is 5(k + 10) > 50, which simplifies to 5k + 50 > 50 and further simplifies to 5k > 0.