Final answer:
By setting up an equation using the contributions of Charlie and Alvin and the condition that Bernie pays the remaining amount, we find that the total cost of the pizza is $24.
Step-by-step explanation:
We are given that Charlie can contribute $2.40, and Alvin agrees to pay 40% of the total cost. We'll denote the total cost of the pizza as 'C'. Bernie is willing to pay his 'fair share', which can be interpreted as the remaining amount after Alvin and Charlie have contributed their parts.
From Alvin's contribution, we know:
- Alvin's contribution = 40% of C = 0.40C
Charlie's contribution is $2.40, so Bernie's contribution plus Alvin's contribution would make up the rest.
Therefore, we can write the equation for the total cost as:
- Charlie's contribution + Bernie's contribution + Alvin's contribution = Total Cost
- $2.40 + Bernie's contribution + 0.40C = C
To find Bernie's contribution, we rearrange the equation:
- Bernie's contribution = C - $2.40 - 0.40C
- Bernie's contribution = 0.60C - $2.40
The fact that Bernie is paying the rest implies that Charlie's and Alvin's contributions must add up to Bernie's contribution, so:
- $2.40 + 0.40C = 0.60C - $2.40
- Adding $2.40 on both sides, we get $2.40 + $2.40 + 0.40C = 0.60C
- Combining like terms, we get $4.80 = 0.60C - 0.40C
- $4.80 = 0.20C
- Dividing by 0.20, we find C = $4.80 / 0.20
- C = $24
Thus, the total cost of the pizza was $24.