Answer:
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
