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. which of the following are true? select all that apply. 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 2(a – 4) + 3a = 48. e. the cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.

We want to find a system of equations, and by solving that system we will be able to see which statements are true.

We will see that options A, C, and E are true.

We know that:

Venetta buys 2lb of pistachios

Venetta buys 3 lb of almonds.

Let's define the variables:

x = price per pound of pistachios

y = price per pound of almonds.

Now we also know that:

"The pistachios cost $4 more per pound than the almonds."

This can be written as:

"She pays a total of $48"

This can be written as:

So a system of equations:

To solve this system, the first thing we need to do is isolate one of the variables in one of the equations, particularly we can see that x is already isolated in the first equation, so we can skip that step.

Now we can replace the isolated variable in the other equation to get:

now we can solve this for y:

now that we know this, we can use:

now that we know:

y = $8

x = $12

Let's see which statements are true:

A) One pound of pistachios plus 1 pound of almonds cost $20.

True, $8 + $12 = $20.

B)  The pistachios cost twice as much per pound as the almonds.

False, $12 is not the double of $8.

C) Reducing the number of pounds of almonds by one results in a total cost of $40.

True, one pound less of almonds means $8 less in the price.

D) The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48

Simplifying the expression we get:

2*(a - 4) + 3a = -8 + a = 48

a = 48 + 8 = 52

This clearly does not model the price of one pound of almonds, this statement is false.

E) The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.

Solving the equation we get:

2*p + 3*p - 12 = 48

5*p = 48 + 12 = 60

p = 60/5 = 12

This is true.

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