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 much of each drink was sold?
To determine how much of each drink was sold, let's first assign variables to each of the drinks:
Let "t" represent the number of teas sold.
Let "c" represent the number of coffees sold.
Let "h" represent the number of hot chocolates sold.
Based on the given information, we can set up three equations:
1. The total number of drinks sold is 20250:
t + c + h = 20250
2. 20 more coffee were sold than hot chocolate:
c = h + 20
3. 30 more coffee were sold than tea:
c = t + 30
We can use these equations to solve for the values of t, c, and h.
We'll start by using equation 3 to substitute c in equations 1 and 2:
t + (t + 30) + h = 20250 (from equation 3)
2t + h = 20250 - 30
2t + h = 20220
Now, we'll substitute c in equation 2 with h + 20:
h + 20 = h + 20
c = h + 20
Substituting c = h + 20 in equation 1:
t + (h + 20) + h = 20250 (from equation 2)
2h + t + 20 = 20250
2h + t = 20230
Now we have two equations with two variables:
2t + h = 20220
2h + t = 20230
We can solve this system of equations using substitution or elimination methods.
Let's solve it using the elimination method.
Multiplying the first equation by 2:
4t + 2h = 40440
Now subtracting the second equation from the first:
(4t + 2h) - (2h + t) = 40440 - 20230
3t = 20210
t = 20210 / 3
t ≈ 6736.67
Since the number of drinks sold must be a whole number, let's round t down to the nearest whole number:
t ≈ 6736
Now plugging the value of t back into equation 2:
2h + 6736 = 20230
2h = 20230 - 6736
2h = 13494
h = 13494 / 2
h = 6747
Finally, plugging the value of h back into equation 3:
c = t + 30
c = 6736 + 30
c = 6766
Therefore, approximately 6736 teas, 6766 coffees, and 6747 hot chocolates were sold.