Danielle sells cupcakes. The first 10 cupcakes a customer purchases costs x dollars each. Every cupcake purchased after 10, each cost 50% of x. If Lucy spent $21.00 on 11 of Danielle’s cupcakes, what is the value of x?
To find the value of x, we can set up an equation based on the given information.
Let's assume the cost of the first 10 cupcakes is x dollars each. Then, for every cupcake purchased after 10, each costs 50% of x.
We know that Lucy spent $21.00 on 11 cupcakes. This means that the first 10 cupcakes cost x dollars each, and the 11th cupcake (purchased after the first 10) costs 50% of x.
The cost of the first 10 cupcakes = 10x
The cost of the 11th cupcake = 0.5x
So, the total cost of 11 cupcakes is: 10x + 0.5x = $21.00
Combining like terms, we get: 10.5x = $21.00
To find the value of x, we can divide both sides of the equation by 10.5:
x = $21.00 / 10.5
Simplifying, we find:
x = $2.00
Therefore, the value of x is $2.00.
The first 10 cupcakes cost x dollars each for a total cost of 10*x = <<10*x=10x>>10x dollars.
The next cupcake cost 50% of x which is x/2 = 1/2*x
The total cost of 11 cupcakes is 21 dollars.
The first 10 cupcakes cost 10x dollars and the next one cost x/2 for a total of 10x + x/2 = <<10*x+x/2=10.5x>>10.5x dollars.
If 10.5x = 21 then x = 21/10.5 = <<21/10.5=2>>2. Answer: \boxed{2}.