A woman bought a number of items for $40. She realized that if she had bought 5 more items for the same money, she would have paid $4 less per item. How many items did she buy?

Answer 1

Let n = the number of items she bought.

Let p = the price per item.

So np=40

And (n+5)(p-4) = 40

n=40/p

continue from here

Answer 2

Let x be the number of items purchased for $40 for an average price of $p for each item

So xp=40

If the number of items go up by 5, the the average price goes down by $4 (the person bought cheaper items--that is the customer did NOT just add 5 more items because that would have increased the total price!)

So (x+5)(p-4) = 40.

Can you finish from here?