no. of prizes is five times the cost of each prize. if the cost of each prize is reduced by 2 then 12 more prizes can be purchased find no. of prizes and cost of each prize. step by step answer

let no of prizes be x
let cost of each prize be y
as per 1st condition x=5*y
total cost of prize is x*y
if cost is reduced by , i.e y-2
​then no of prizes that can be bought x+12
total cost remains the same i.e. (x+12)*(y-2)=xy
​xy-2x+12y-24=xy
​12y-2x=24
put x=5y from 1st condition
12y-2*5y=24
2y=24
y=12
so x=60
cost of each prize is 12
total no of prize is 60
 

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