At the fish counter, salmon was selling for $9.60 a pound, whitefish for $7.20 a pound, swordfish for $8.40 a pound, and haddock for $6.90 a pound. Sasha bought 3/4 Ib. of fish for $5.40. What fish did he choose?
Let's say Sasha bought x pounds of salmon.
Since salmon sells for $9.60 a pound, the cost of the salmon is 9.6x dollars.
Let's say Sasha bought y pounds of whitefish.
The cost of the whitefish is 7.2y dollars.
Let's also say Sasha bought z pounds of swordfish.
The cost of the swordfish is 8.4z dollars.
Finally, Sasha bought w pounds of haddock.
The cost of the haddock is 6.9w dollars.
Since he bought 3/4 Ib. of fish for $5.4, we can say x + y + z + w = 5.4/(3/4) = 5.4*4/3 = 7.2 pounds.
From the information above, w = 7.2 - x - y - z.
Substituting the equation above to the equation for the cost of the fish, the total cost of the fish is 9.6x + 7.2y + 8.4z + 6.9(7.2 - x - y - z) = 5.4.
Simplifying the equation, 9.6x + 7.2y + 8.4z + 49.68 - 6.9x - 6.9y - 6.9z = 5.4.
Collecting like terms, 2.7x + 0.3y + 1.5z = -44.28.
Since all the coefficients are decimals, let's multiply the equation by 10 to eliminate the decimal places: 27x + 3y + 15z = -442.8.
From the equation above, we know that the left side of the equation is divisible by 3.
Since -442.8 is divisible by 3, x + y + z must be divisible by 3.
Let's analyze the options:
- If Sasha buys 1 pound of salmon, 2 pounds of whitefish, and 1 pound of swordfish, the sum is 1 + 2 + 1 = 4 which isn't divisible by 3.
- If Sasha buys 2 pounds of salmon, 1 pound of whitefish, and 1 pound of swordfish, the sum is 2 + 1 + 1 = 4 which isn't divisible by 3.
- If Sasha buys 0 pounds of salmon, 3 pounds of whitefish, and 1 pound of swordfish, the sum is 0 + 3 + 1 = 4 which isn't divisible by 3.
- If Sasha buys 0 pounds of salmon, 2 pounds of whitefish, and 2 pounds of swordfish, the sum is 0 + 2 + 2 = 4 which isn't divisible by 3.
- If Sasha buys 1 pound of salmon, 0 pounds of whitefish, and 3 pounds of swordfish, the sum is 1 + 0 + 3 = 4 which isn't divisible by 3.
- If Sasha buys 0 pounds of salmon, 0 pounds of whitefish, and 4 pounds of swordfish, the sum is 0 + 0 + 4 = 4 which isn't divisible by 3.
We can conclude that there is no combination of salmons, whitefish, swordfish, and haddocks that Sasha could buy.