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24 January, 02:13

For a camping trip, Blake wants to make a trail mix of almonds, walnuts and raisins. He wants one part almonds, two parts walnuts, and three parts raisins. Almonds cost $15 per pound, walnuts cost $10 per pound, and raisins cost $5 per pound. Blake has $30 to spend on the trail mix. The equation 15x + 10 (2x) + 5 (3x) = 30 models the pounds, x. How many pounds of trail mix can Blake buy?

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  1. 24 January, 04:45
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    We are given equation: 15x + 10 (2x) + 5 (3x) = 30.

    Where x represents number of pounds.

    Almost cost = $15 per pound.

    Therefore, cost of x pounds of almonds = 15*x = 15x.

    Walnuts cost = $10 per pound.

    We have two parts walnuts.

    Therefore, cost of 2 times x pounds of walnuts = 10 * (2x).

    Raisins cost = $5 per pound.

    We are given three parts raisins.

    Therefore, cost of 3 times x pounds of raisnis = 5 * (3x).

    Total money spent = $30.

    Let us solve the given equation for x now.

    15x + 10 (2x) + 5 (3x) = 30.

    15x + 20x + 15x = 30.

    Combining like terms, we get

    50x = 30.

    Dividing both sides by 50, we get

    50x/50 = 30/50.

    x=0.6

    Therefore, number of pounds of Almonds = 0.6 pound.

    Walnuts = 2x = 2*0.6 = 1.20 pounds.

    Raisins = 3x = 3*0.6 = 1.80 pounds.

    Therefore, total number of pounds of trail mix can Blake buy = 0.6 + 1.20 + 1.80 = 3.60 pounds.
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