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6 January, 09:46

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?

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  1. 6 January, 10:20
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    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
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