Question

Q2. In a camp food was enough for 400 people for 23 days. If 60 more people joined the camp, find the number of days the food will last?

Q3. Given that y is directly proportional to x and that y= 40 when x= 200, find the value of
(a) y when x= 15
(b) x when y= 8

Q4. If y is inversely proportional to x and that y= 8 when x= 30, find the value of:

(a) the value of y when x= 4
(b) the value of x when y= 360​
​

Answer 1

Q2)

We have food for 400 people, and it will last for 23 days.

Then we have an inverse relation, where the number of days decreases as the number of people increases, this means that we have a relationship like:

23 days = K/400 people.

Then we get:

(23 days)*(400 people) = K = 9200 days*people.

Now if we increase the number of people by 60, we get.

people = 460

Then the number of days that this will last is:

D = (9200 days*people)/460 people = 20 days.

The food will last for 20 days.

Q3) We have a proportional relationship (y = k*x) such that y = 40 when x = 200, then we get:

40 = k*200

With this, we can find the value of k

40/200 = k = 0.2

Then the proportional relationship is:

y = 0.2*x

a) We need to replace x by 15.

y = 0.2*15 = 3

y = 3

b) We need to replace y by 8.

8 = 0.2*x

8/0.2 = x = 40

x = 40

Q3) y is inversely proportional to x (y = k/x), and y = 8 when x = 30.

Then we get:

8 = k/30

Then the value of k is:

8*30 = k = 240

then the relationship is:

y = 240/x

a) we need to replace x by 4

y = 240/4 = 60

y = 60

b) we need to replace y by 360

360 = 240/x

360*x = 240

x = 240/360 = 0.666...

x = 0.666...