Distance revenue

Question

A woman bought a number of items for $90. She realized that if she had bought 25 more items for the same money, she would have paid $15 less per item. How many items did she buy?

Answer 1

number of item she buy = n

cost per item = 90/n

 

she had bought (n+25 )items for the same money then

cost per item  would be (90/n) - 15

 

so we can write

cost of item = cost of item

90 /(n+25) = (90/n)-15

 

multiply both side with n(n+25)

90n = 90(n+25) - 15n(n+25)

90n=90n+2250 -15n² -375n

15n²+375n-2250 =0

 

divide by 50 to equation

n²+25n-150 =0

 

(n+30)(n-5)=0

n=-30 and n=5

n=-30 (-ve answer is not possible) so n=5

So she buy 5 items