If 3 pistachio and 1 walnut weigh the same as 10 peanuts, and 1 pistachio and 6 peanuts weigh the same as 1 walnut, how many peanuts weigh the same as 1 walnut?

7

Step-by-step explanation:

We need to translate all these statements to equations.

First of all, let P be the pistachios, W the walnuts and N the peanuts.

The first statement "3 pistachio and 1 walnut weigh the same as 10 peanuts" can be represented as:

3 P + 1 W = 10 N

The second statement "1 pistachio and 6 peanuts weigh the same as 1 walnut" can be represented as:

1 P + 6 N = 1 W

If we notice, both equations have a similar term: 1 W. The second gives us the equivalence to the weight of 1 walnut, whereas in the first we have the weight of 1 walnut as an unknown variable. Lets replace it!

3 P + 1 W = 10 P

3 P + (1 P + 6 N) = 10 P

4 P + 6 N = 10 P

We now need to sum (-4P) in both sides to eliminate the 4 P on the left:

4 P + 6 N - 4P = 10 P - 4 P

6 N = 6 P

Dividing both sides by 6:

N = P

Now we need an equation that relates walnuts to peanuts. Lets replace N=P on our firts equation:

3 P + 1 W = 10 P

3 N + 1 W = 10 N

Summing  (-3 N) in both sides:

3 N + 1 W - 3N = 10 N - 3N

1 W = 7 N

So, 1 walnut weights the same that 7 peanuts

d is correct

step-by-step explanation:

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: