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17 May, 23:42

How many pounds of peanuts costing $1.90/Ib and raisins costing $2.50/Ib should Mr. Bruckner mix to make 12 Ib of a trail mix that costs $2.05/ib

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  1. 18 May, 00:06
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    Let p and r be the amount of peanuts and raisins respectively.

    p+r=12, p=12-r

    We are given that:

    (1.9p+2.5r) / 12=2.05, using p found above in this equation:

    (1.9 (12-r) + 2.5r) / 12=2.05 perform indicated multiplication on left side

    (22.8-1.9r+2.5r) / 12=2.05 combine like terms on left side

    (22.8+0.6r) / 12=2.05 multiply both sides by 12

    22.8+0.6r=24.6 subtract 22.8 from both sides

    0.6r=1.8 divide both sides by 0.6

    r=3, and since p=12-r

    p=12-3

    p=9

    So Mr. Bruckner will need to mix 9 pounds of peanuts with 3 pounds of raisins to make a 12 pound mixture which costs $2.05 per pound.
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