Number of items sold by Shelley = 3 items.
Let us assume cost of each item sold by Shelley = $ x each.
Total cost of 3 items for Shelly sold = 3*x = 3x.
Number of items sold by Billy Bob = 4 items.
The cost of each item sold by Billy Bob = $2.25 less than the items that Shelley bought = $(x-2.25) each.
Total cost of 4 items for Billy Bob sold = 4*(x-2.25) = 4(x-2.25).
Both Shelley and Billy Bob paid the same amount of money. So, we can setup an equation now.
a) Total cost of 4 items for Billy Bob sold=Total cost of 3 items for Shelly sold.
4(x-2.25) = 3x
b) Solving equation for x now.
Distributing 4 over (x-2.25), we get
4x - 4*2.25 = 3x.
4x -9 = 3x.
Adding 9 on both sides, we get
4x -9+9 = 3x+9
4x =3x+9.
Subtracting 3x from both sides, we get
4x-3x =3x-3x+9.
x = 9.
c) Checking the solution of the equation by plugging x=9 in equation we got above.
4(x-2.25) = 3x => 4(9-2.25)= 3*9
=> 4*6.75 = 27
=> 27 = 27.
We got left side = right side. So the solution x=9 is correct.
d) The cost of each item sold by Billy Bob = 9-2.25 = $6.75
Therefore, the cost of each item sold by Shelley is $9 and cost of each item sold by Billy Bob is $6.75.
