Question

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.

Answer 1

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