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 lb. of fish for $5.40. What fish did he choose?
A. Salmon
B. Whitefish
C. Swordfish
D. Haddock
Let's assume Sasha bought x pounds of salmon, y pounds of whitefish, z pounds of swordfish, and w pounds of haddock.
According to the problem, we have the following equations:
x + y + z + w = 3/4 (Sasha bought 3/4 lb. of fish)
9.6x + 7.2y + 8.4z + 6.9w = 5.4 (the total cost of the fish is $5.40)
From the given equations, we can see that Sasha didn't buy any haddock because the price per pound for haddock is the lowest. Therefore, w = 0.
Now, let's substitute w = 0 into the equations:
x + y + z + 0 = 3/4
9.6x + 7.2y + 8.4z + 6.9(0) = 5.4
Simplifying the equations further:
x + y + z = 3/4
9.6x + 7.2y + 8.4z = 5.4
Now, let's solve the equations to find the values of x, y, and z.
Using the second equation:
9.6x + 7.2y + 8.4z = 5.4
Let's multiply the first equation by 9.6 to make the coefficients of x the same:
9.6(x + y + z) = 9.6(3/4)
9.6x + 9.6y + 9.6z = 7.2
Subtracting the new equation from the second equation:
(9.6x + 7.2y + 8.4z) - (9.6x + 9.6y + 9.6z) = 5.4 - 7.2
-2.4y - 1.2z = -1.8
2.4y + 1.2z = 1.8 (multiplying both sides by -1 to change the signs)
Now, we have a system of two equations:
2.4y + 1.2z = 1.8 (Equation 1)
2.4y - 1.2z = 1.8 (Equation 2)
Adding Equation 1 and Equation 2:
(2.4y + 1.2z) + (2.4y - 1.2z) = 1.8 + 1.8
4.8y = 3.6
y = 3.6/4.8
y = 3/4
Substituting the value of y into Equation 1:
2.4(3/4) + 1.2z = 1.8
1.8 + 1.2z = 1.8
1.2z = 1.8 - 1.8
1.2z = 0
z = 0/1.2
z = 0
Therefore, y = 3/4 and z = 0.
Substituting y = 3/4 and z = 0 into the first equation:
x + (3/4) + 0 = 3/4
x + (3/4) = 3/4
x + 3/4 = 3/4 - 3/4
x + 3/4 = 0
Therefore, x = 0 - 3/4
x = -3/4
Since x, y, and z represent the pounds of salmon, whitefish, and swordfish respectively, we cannot have negative values. Therefore, Sasha did not choose any of the available fish options (salmon, whitefish, swordfish, or haddock).
The correct answer is none of the above.
It has to be one of the above.
Apologies for the confusion in the previous response. Let's recalculate:
Since Sasha bought a total of 3/4 lb of fish for $5.40, we can set up the equation:
9.6x + 7.2y + 8.4z + 6.9w = 5.4
where x, y, z, and w represent the pounds of salmon, whitefish, swordfish, and haddock respectively.
Now let's check the given options:
A. Salmon: If Sasha bought 1 lb of salmon (x = 1), the cost would be 9.6 * 1 = $9.60, which is more than $5.40 spent.
B. Whitefish: If Sasha bought 3/4 lb of whitefish (y = 3/4), the cost would be 7.2 * (3/4) = $5.40, which matches the amount spent. This is a potential solution.
C. Swordfish: If Sasha bought 2/3 lb of swordfish (z = 2/3), the cost would be 8.4 * (2/3) = $5.60, which is more than $5.40 spent.
D. Haddock: If Sasha bought 4/5 lb of haddock (w = 4/5), the cost would be 6.9 * (4/5) = $5.52, which is more than $5.40 spent.
Therefore, the only fish option that matches Sasha's purchase of 3/4 lb for $5.40 is B. Whitefish.
The answer is B. Whitefish.
To determine which fish Sasha chose, we need to determine the cost of the fish purchased and compare it to the prices per pound of each type of fish.
Let's assume Sasha chose fish X.
Since Sasha purchased 3/4 lb. of fish, the cost per pound of fish X would be $5.40 / (3/4) = $5.40 * (4/3) = $7.20.
Now, let's compare this cost per pound of fish X with the prices per pound of each type of fish:
- Salmon: $9.60 a pound
- Whitefish: $7.20 a pound
- Swordfish: $8.40 a pound
- Haddock: $6.90 a pound
We can see that the cost per pound of fish X, which is $7.20, matches the cost per pound of Whitefish.
Therefore, Sasha chose Whitefish.
Hence, the correct answer is:
B. Whitefish