A carpenter purchased 50 ft of redwood and 90 ft of pine for a total cost of $286. A second purchase, at the same prices, included 100 ft of redwood and 70 ft of pine for a total cost of $418. Find the cost per foot of redwood and of pine.


redwood

      dollars per foot

pine

      dollars per foot

Let's define the cost per foot of redwood as $ x $ (in dollars) and the cost per foot of pine as $ y $ (in dollars).

We are given the following two pieces of information from the carpenter's purchases:

1. The first purchase included 50 feet of redwood and 90 feet of pine for a total of $286:
\[
50x + 90y = 286
\]

2. The second purchase included

A carpenter purchased 50 ft of redwood and 90 ft of pine for a total cost of $286. A second purchase, at the same prices, included 100 ft of redwood and 70 ft of pine for a total cost of $418. Find the cost per foot of redwood and of pine.

Learn how to find the cost per foot of redwood and pine by solving a system of linear equations. The problem involves algebraic concepts and is suitable for students in Grades 9-11. Two equations are used to determine the price per foot based on the total costs of different wood purchases.

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