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