Question

Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a total of $48. Select all the correct statements about this situation.
A. One pound of pistachios plus 1 pound of almonds cost $20.
B. The pistachios cost twice as much per pound as the almonds.
C. Reducing the number of pounds of almonds by one results in a total cost of $40.
D. The cost a, in dollars, of 1 pound of almonds is modeled by the equation 2(a − 4) + 3a = 48.
E. The cost p, in dollars, of 1 pound of pistachios is modeled by the equation 2p + 3(p − 4) = 48.

Answer 1

Correct: A, C, and E.

Work:
Let a = price per lb of almonds, p = price per lb of pistachios. p = a + 4 and 2p + 3a = 48.
Substitute: 2(a+4)+3a = 48 → 5a + 8 = 48 → a = 8, so p = 12.

- A: 1 lb pistachios + 1 lb almonds = 12 + 8 = 20 → true.
- B: 12 is not twice 8 → false.
- C: Removing one lb of almonds reduces total by $8 to $40 → true.
- D: 2(a − 4) + 3a = 48 gives the wrong relation (would imply pistachios cheaper) → false.
- E: 2p + 3(p − 4) = 48 correctly models p with almonds = p − 4 → true.