A carpenter bought wood

Question

A carpenter purchased 70 ft of redwood and 90 ft of pine for a total cost of $371. A second purchase, at the same prices, included 100 ft of redwood and 60 ft of pine for a total cost of $434. Find the cost per foot of redwood and of pine.

Answer 1

70r + 90p = 371

100r+ 60p= 434

multiply 1st equation by 10, 2nd by 7

700r +420p = 7(434)=3038

700r +900p = 3710

subtract to eliminate one variable

480p = 3710-3038= 672

p = 672/480 = $1.40 per foot for pine

70r +90(1.4) =371

70r = 371-90-36=245

r = 245/70 = $3.50 per foot for redwood

check the answers

100(3.5)+60(1.4)

=350+84

=434

70(3.5)+90(1.4)

=245 +126

= 371