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17 September, 13:08

A carpenter purchased 60 ft of redwood and 90 ft of pine for a total cost of $315. A second purchase, at the same prices, included 100 ft of redwood and 60 ft of pine for a total cost of $408. Find the cost per foot of redwood and of pine.

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  1. 17 September, 13:23
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    Let the price of a foot of redwood cost $r and a foot of pine cost $p

    60r + 90p = $315

    100r + 60p = $408

    This forms simultaneous equation and solving it by substitution:

    100 (60r + 90p = $315) ... (1)

    60 (100r + 60p = $408) ... (2)

    6000r + 9000p = $31500 ... (1)

    6000r + 3600p = $24480 ... (2)

    Subtracting (2) from (1):

    5400p = $7020

    p = $1.3

    and r = ($315 - (90 x 1.3)) / 60 = $198/60 = $3.3

    A foot of redwood costs $1.3

    A foot of pine costs $3.3
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