At a school camp there is enough food for 150 students for 5 days. a) How long would the food last if there were only 100 students? b) If the food ran out after only 4 days, how many students attended the camp?

The correct answer is: 187

Let the number of days be represented as x and the number of students be represented as y. The number of days will decrease if the number of students are increased so we can conclude that y is in inverse relationship with x. Let’s say the proportional relationship is given as
y =   ……..(1)
It is given that there is enough food for 150 students for 5 days i.e. x = 5 and y = 150. Putting the values in equation (1)
150 =
k = 150 × 5 = 750
a)
We are asked to find the number of days the food will last if there are 100 students. So, y = 100 and we need to find x. Putting the values in equation (1)
100 =
Now, put the value of k = 750
d = 
d = 7.5 days
Final Answer:
Hence, the food will last for 7.5 days if there are 100 students.
b)
We are asked to find the number of students if the food lasts for 4 days. So, x = 4 and we need to find y. Putting the values in equation (1)
y = 
Now, put the value of k = 750
y = 
y = 187.5 = 187 students
(Number of Students can’t be students)
Final Answer:
Hence, if the food lasts for 4 days, the number of students will be 187.