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.

If you want to learn more, you can read:

link

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?

answer: the answer is simply nothing.

step-by-step explanation: because there is no ending to this question

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