A lady buys three items in the shop. The total cost of the items is $90.09.It so happens that if the prices are multiplied they still come to $90.09! What are the prices?
To find the prices of the three items, we can set up a system of equations. Let's assume the prices of the three items are x, y, and z (in dollars).
From the given information, we know that the total cost of the three items is $90.09. Therefore, we can write the equation:
x + y + z = 90.09 (Equation 1)
We are also given that if the prices are multiplied together, they still come to $90.09. This can be written as another equation:
xyz = 90.09 (Equation 2)
To solve this system of equations, we can use substitution. Solve for one variable in either Equation 1 or Equation 2 and substitute that value into the other equation.
Let's solve Equation 1 for z:
z = 90.09 - x - y
Substitute this value of z into Equation 2:
x * y * (90.09 - x - y) = 90.09
Simplify and solve this equation for x and y. This is a quadratic equation, so rearrange the equation and set it equal to zero:
x * y * (90.09 - x - y) - 90.09 = 0
Multiply out the terms:
90.09xy - xy^2 - x^2y - 90.09 = 0
Rearrange the terms:
xy^2 + x^2y - 90.09xy + 90.09 = 0
Now, this is a quadratic equation in terms of x and y. We can solve it by factoring or using the quadratic formula. After finding the values of x and y, substitute them back into Equation 1 to find the value of z.
The calculated values of x, y, and z will be the prices of the three items purchased by the lady.