Betty and Wilma both sell cookies to earn money for a trip. Betty charges $2 per cookie and Wilma charges $1.50 per cookie. If Betty has to pay $1.50 for her secret ingredient, how many cookies, x, must they each sell before they have the same amount of money?
Let's assume Betty sells x cookies.
The amount of money Betty earns from selling x cookies is 2 * x = <<2*x=2x>>2x dollars.
Betty has to pay $1.50 for her secret ingredient, so the amount of money Betty is left with is 2x - $1.50.
Wilma charges $1.50 per cookie, so to earn the same amount of money as Betty, she needs to sell 2x - $1.50 / $1.50 = (2x - $1.50) / $1.50 = 1.333...x cookies.
Since we can't sell a fraction of a cookie, they must each sell x = 2 * x - $1.50 / $1.50 = 4x - $1.50 / $1.50 = 3.5x - $1.50 / $1.50 = 3.5 cookies to have the same amount of money. Answer: \boxed{3}.
Let's set up an equation to solve for the number of cookies, x, that Betty and Wilma must each sell to have the same amount of money.
Betty's earnings (B) can be represented as:
B = 2x - 1.50
Wilma's earnings (W) can be represented as:
W = 1.50x
Since we want both Betty and Wilma to have the same amount of money, we can set B equal to W and solve for x:
2x - 1.50 = 1.50x
First, let's subtract 1.50x from both sides:
2x - 1.50x - 1.50 = 0
Combining like terms:
0.50x - 1.50 = 0
Next, add 1.50 to both sides:
0.50x = 1.50
Finally, divide both sides by 0.50:
x = 1.50 / 0.50
Simplifying:
x = 3
Therefore, Betty and Wilma must each sell 3 cookies in order to have the same amount of money.
To find the number of cookies each must sell before they have the same amount of money, we can set up an equation.
Let's assume Betty sells x cookies. Wilma sells y cookies.
Given that Betty charges $2 per cookie and Wilma charges $1.50 per cookie, the amount of money Betty makes is given by 2x, and the amount of money Wilma makes is given by 1.5y.
Betty also has to pay $1.50 for her secret ingredient. So, her net amount of money is 2x - 1.50.
We want to find the point at which Betty and Wilma have the same amount of money, so we set up the equation:
2x - 1.50 = 1.5y
Now, we solve this equation for x:
2x - 1.50 = 1.5y
2x = 1.5y + 1.50
x = (1.5y + 1.50)/2
Since we want to find the x value where Betty and Wilma have the same amount of money, we need to find a whole number value for x. This means that for each whole number value of y, we must find a corresponding whole number value of x.
By plugging in different whole number values for y, we can find the corresponding value for x. Let's try some values:
For y = 1, x = (1.5*1 + 1.50)/2 = 2.25/2 = 1.125 (not a whole number)
For y = 2, x = (1.5*2 + 1.50)/2 = 4.5/2 = 2.25 (not a whole number)
For y = 3, x = (1.5*3 + 1.50)/2 = 6.75/2 = 3.375 (not a whole number)
For y = 4, x = (1.5*4 + 1.50)/2 = 9/2 = 4.5 (not a whole number)
For y = 5, x = (1.5*5 + 1.50)/2 = 11.25/2 = 5.625 (not a whole number)
We can see that for these values of y, the corresponding values of x are not whole numbers. Therefore, there is no whole number solution to this problem.