The weekly expenses of a hostel are partly constant and partly vary directly as the number of inmates . If the expenses are rs 2000 when the number of inmates is 120 and rs 1700 when the number is 100 . Find the number of inmates when the expenses are rs 1880 .

Explanation

Let the expenses be rs y and the number of inmates = x.
As per question , y =`k_1 +k_2x……..(1)`
[where `k_1 =constant and k_2 ne 0= ` variation constant ]
As per question, if x =120 , then y 2000.
`therefore` from (1) we get , 2000 =`k_1 +k_2xx120`
or, `k_1+120k_2=2000......(2)`
Again , if x =100,then y =1700.
`therefore` from (1) we get ,1700=`k_1+k_2xx100`
or, `k_1+100k_2=1700........(3)`
Now , subtracting (3) from (2) we get ,
`20k_2=300 or, k_2=15` .
`therefore` from (2) we get ,` k_1 +120 xx15 =2000`
`rArrk_1=2000-1800`
`rArr k_1 =200`
`therefore` from (1) we get ,y 200 +15x........(4)
so, putting y = 1880 in (4) we get , 1880 =200 +15x
or, 15x =1680 or, x=`(1680)/(15)=112` .
Hence the required number of inmates =112.