this is a math question

Question

A carpenter purchased 60 ft of redwood and 70 ft of pine for a total cost of $287. A second purchase, at the same prices, included 90 ft of redwood and 60 ft of pine for a total cost of $381. Find the cost per foot of redwood and of pine.

Answer 1

Let R be the price per foot for redwood, P the price per foot of Pine.

The first purchase is 60R + 70P = $287

The second 90R + 60P = $381

You have two unknowns and two equations, so you can solve by simultaneous equations.

Multiply the first by 3 and the second equation by 2

180R + 210P = $861

180R + 120P = $762

Subtract 90P = 99

Pine sells for $1.10 per foot

Substituting into the first equation 60R + 70($1.10) = $287

60R + $77 = $287

60R = $210

R = $3.50 per foot

I always double check my answers

60 at $3.50 + 70 at $1.10 = $287 90 @ $3.50 + 60 at $1.10 = $381

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