Final answer:
John's, Sally's, and Elijah's equations are set up using variables for the prices of different sushi rolls. Solving these equations gives us the price for one California roll ($5.95), one Ahi Tuna ($6.50), and one Eel Roll ($7.25). The total cost for buying 3 Ahi Tuna, 2 California Rolls, and 1 Eel Roll is $38.65.
Step-by-step explanation:
To solve the problem, we need to set up equations based on the prices of the sushi rolls and the totals spent by John, Sally, and Elijah. Let's use the variables A for the price of one Ahi Tuna roll, C for the price of one California roll, and E for the price of one Eel roll.
Based on this, we have the following equations:
John's Equation: 2A + 1C + 1E = $26.20
Sally's Equation: 3C = $17.85
Elijah's Equation: 3A + 2C = $31.40
To find the cost of one California roll (C), we take Sally's total and divide by the number of rolls:
C = $17.85 / 3 = $5.95
Now, we can plug in the cost of C into John's and Elijah's equations to find A and E.
For John's Equation, we have:
2A + $5.95 + E = $26.20
- Subtract $5.95 from both sides to isolate 2A + E:
2A + E = $20.25
For Elijah's Equation, plugging in the cost of C gives:
3A + 2($5.95) = $31.40
- Simplify this to find the price of A:
3A + $11.90 = $31.40
3A = $19.50
A = $6.50
Now we know the cost of A and can use it along with the cost of C in John's equation to find E.
2($6.50) + E = $20.25
E = $20.25 - $13.00
E = $7.25
Finally, we find the total cost for 3 Ahi Tuna, 2 California Rolls, and 1 Eel Roll:
Total = 3A + 2C + E
Total = 3($6.50) + 2($5.95) + $7.25
Total = $19.50 + $11.90 + $7.25
Total = $38.65