Answer:
A. Combining one pound of pistachios with one pound of almonds costs $20.
C. Decreasing the almond quantity by one pound leads to a total price of $40.
E. The price p (in dollars) per pound of pistachios is represented by the equation 2p + 3(p – 4) = 48.
Step-by-step explanation:
Let:
x = cost per pound of pistachios
y = cost per pound of almonds
We know that
x = y + 4 (Equation A)
2x + 3y = 48 (Equation B)
Substitute x from Equation A into Equation B:
2(y + 4) + 3y = 48
2y + 8 + 3y = 48
5y = 48 – 8
y = 8
Find x:
x = 8 + 4 = 12
Therefore, pistachios cost $12 per pound and almonds cost $8 per pound.
Verify the statements:
Case A) One pound of each equals $20.
True, since 12 + 8 = 20.
Case B) Pistachios cost twice as much as almonds.
False, because 2 × 8 = $16 ≠ $12.
Case C) Reducing almond pounds by 1 yields $40 total.
True, as 2(12) + 2(8) = 24 +16 = 40.
Case D) The almond cost modeled by 2(a – 4) + 3a = 48.
False; it should be 2(a + 4) + 3a = 48.
Case E) The pistachio cost modeled by 2p + 3(p – 4) = 48.
True, since p = a + 4 implies a = p – 4.
