Answer:
A. One pound of pistachios plus 1 pound of almonds cost $20
C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.
E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
Step-by-step explanation:
Let
x ----> the cost of one pound pistachios
y ----> the cost of one pound of almonds
we know that
x=y+4 -----> equation A
2x+3y=48 -----> equation B
substitute equation A in equation B and solve for y
2(y+4)+3y=48
2y+8+3y=48
5y=48-8
y=8
Find the value of x
x=8+4 =12
therefore
The cost of one pound pistachios is $12 and the cost of one pound of almonds is $8
<em>Verify all statements</em>
case A) One pound of pistachios plus 1 pound of almonds cost $20.
Is True
x+y=$12+$8=$20
case B) The pistachios cost twice as much per pound as the almonds
Is false
Because
2y=2(8)=$16
$16≠$12
case C) Reducing the number of pounds of almonds by 1 results in a total cost of $40
Is True
Because
2x+2y=2(12)+2(8)=$40
case D) The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48.
Is false
The equation will be
2(a + 4) + 3a = 48.
case E) The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48
Is true
Because
p=a+4
Solve for a
a=p-4
