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.
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?
1 answer