Answer: Let's use algebra to solve this problem. Let's assume that the cost of each toy car is "x," and Alvin had "y" dollars initially.
According to the given information:
If Alvin bought three toy cars, he would have $50 left. This can be represented by the equation: y - 3x = 50.
If Alvin bought seven toy cars, he would have $6 left. This can be represented by the equation: y - 7x = 6.
Now, we have a system of two equations:
y - 3x = 50
y - 7x = 6
To solve this system, we can use the method of substitution or elimination. Let's use the elimination method:
Subtract equation (2) from equation (1):
(y - 3x) - (y - 7x) = 50 - 6
y - 3x - y + 7x = 44
4x = 44
Now, solve for "x":
x = 44 / 4
x = 11
Now that we know the cost of each toy car is $11, we can find the value of "y" (the amount Alvin had initially) by substituting the value of "x" into either equation (1) or (2):
y - 3x = 50
y - 3(11) = 50
y - 33 = 50
y = 50 + 33
y = 83
So, Alvin had $83 initially.