Answer:
Ben bought 11 cheese pizzas, 16 pepperoni pizzas and 9 supreme pizzas
Step-by-step explanation:
We can solve this problem with a equation system. I will abbreviate the amount of cheese pizzas he buyed as C, the amount of pepperoni ones as P, and the amount of supreme ones as S. I will also remove the $ notation
The system is given as follows
We can easily replace 11P with 16C in equation 2, obtaining
8C + 16C + 14S = 390
24C + 14S = 390
S = (390- 24C)/14 = 195/7 - 12/7 C
Note that, also from equation 3, we have that
11P = 16 C
P = 16/11 C
Now, we can obtain the value of C using equation 1 replacing S and P with the founded values
C+P+S = 36
C + 16/11 C + 195/7 - 12/7 C = 36
C + 16/11 C - 12/7 C = 36-195/7 = 57/7
Taking C as common factor we obtain
C (1+16/11-12/7) = 57/7
C * 57/77 = 57/7
C = (57/7) / (57/77) = 11
Now, we replace this value in the formula we obtain for P and S
P = 16/11 * C = 16/11 * 11 = 16
S = 195/7 - 12/7 * 11 = 63/7 = 9
Now, we verify:
- C+P+S = 11+16+9 = 36
- 8C + 11P + 14S = 8*11 + 11*16 + 14*9 = 88 + 176 + 126 = 390
- 2(8C) = 2*88 = 176 = 11P
Thus, Ben bought 11 cheese pizzas, 16 pepperoni pizzas and 9 supreme pizzas.
