Answer:
6 large, 12 medium and 18 small
Step-by-step explanation:
Lets call small pizzas s, medium pizzas m and large pizzas l, with its respective prices $10, $15 and $40.
As they sell as many small as medium and large combined we can say that:
s = m + l [eq 1]
Also, as the number of medium is twice the larges we can say that:
m = 2l [eq 2]
Finally, as the get $600 we know that every amount sold multiplied by its price, and summing all together must bring $600:
10s + 15m + 40l = 600 [eq 3]
Lets replace s by its value in eq 1:
10s + 15m + 40l = 10 (m+l) 15m + 40l = 10m +10l + 15m + 40l = 600
25m + 50l = 600
Now we can replace m by its value in eq 2:
25m + 50l = 25 (2l) + 50 l = 50l + 50l = 100l = 600
100l = 600
Now divide both sides by 100:
l = 6
So, 6 large pizzas were sold.
Replace l=6 in eq 2:
m = 6*2
m = 12
12 medium pizzas were sold.
Finally, replace l=6 and m=12 in eq 1
s = m + l = 12 + 6 = 18
And 18 small pizzas were sold.
Lets verify our results in eq. 3:
10*(18) + 15*(12) + 40*(6) = 600
180 + 180 + 240 = 600
360 + 240 = 600 ---> Verified!
