A store sells tea for $1.05, coffee for $1.35 and hot chocolate for $2.25. One day, the store sells 20250 drinks. 20 more coffee are sold than hot chocolate, and 30 more coffee are sold than tea. How many of each drink was sold?

Both the numbers of hot choc and tea are stated in relation to coffee, so I will let the number of cups of coffee be x

then they sold x-20 hot chocs
and they sold x-30 teas
so x + x-20 + x-30 = 20250
3x - 50 = 20250
x = 6766.666

Something is wrong here!
Where does the price of these products enter the picture ?

Check you typing of the problem.

It equals to $20250. does that make a difference?

To solve this problem, we can use a system of equations. Let's assume the number of teas sold is "x," the number of coffees sold is "y," and the number of hot chocolates sold is "z."

We are given three pieces of information:

1. The store sells a total of 20250 drinks. Therefore, we can write the first equation as:
x + y + z = 20250

2. 20 more coffee are sold than hot chocolate. So we can write the second equation as:
y = z + 20

3. 30 more coffee are sold than tea. Thus, the third equation is:
y = x + 30

From equations (2) and (3), we see that y (coffee) appears in both equations. We can solve for it in terms of x by substituting. Let's substitute equation (3) into equation (2):
x + 30 = z + 20

Simplifying this equation, we get:
x - z = -10 [equation (4)]

Now we have three equations:

x + y + z = 20250 [equation (1)]
y = z + 20 [equation (2)]
x - z = -10 [equation (4)]

We can solve this system of equations by substitution or elimination. Let's use substitution to find the values of x, y, and z:

From equation (4), we can rewrite it as:
z = x + 10

Substitute this value back into equation (2):
y = (x + 10) + 20
y = x + 30

Now substitute the values of y and z into equation (1):
x + (x + 30) + (x + 10) = 20250
3x + 40 = 20250

Solve for x:
3x = 20250 - 40
3x = 20210
x = 6736.67

Since we cannot have a fraction of a drink, we need to round x down to the nearest whole number:
x = 6736

Now substitute the value of x back into the equations to find y and z:
y = x + 30
y = 6736 + 30
y = 6766

z = x + 10
z = 6736 + 10
z = 6746

Therefore, 6736 teas, 6766 coffees, and 6746 hot chocolates were sold.