Question

A carpenter purchased 50 ft of redwood and 90 ft of pine for a total cost of $274. A second purchase at the same prices include 80 ft of redwood and 50 ft of pine for a total cost of 335. Find the cost per foot of redwood and of pine

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Answer 1

Redwood: $3.50 per foot

Pine: $1.10 per foot

Explanation:

The manner that should be approach is by using the substitution method.

Therefore using the information from the question:

50 ft of redwood and 90 ft of pine give a total cost of $274

So we use this information and make a equation using x and y, in this case redwood would be x and pine would be y.

`50x + 90y=274`

We do this for the second purchase also...

`80x+50y=335`

Now, we have two equations that are perfect for the usage of the substitution method.

`50x + 90y=274`

`80x+50y=335`

Using one equation, in this case the top one, we must solve for either x or y (in this case we solved for y)

`90y=274-50x`

`(90y)/(90) =(274)/(90) -(50x)/(90)`

`y=(274)/(90) -(50x)/(90)`

Using this equation from above we insert this into the other equation that deals with the second purchase and solve for x now.

`80x+50((274)/(90) -(50x)/(90))=335`

`80x+152.2-27.8x=335`

`80x-27.8x=182.8`

`(52.2x)/(52.2) =(182.8)/(52.2)`

`x=3.50`

This is the cost of redwood so now we use this answer and plug it in either equation in order to get the cost of pine (y).

`50(3.5)+90y=274`

`175+90y=274`

`(90y)/(90)=(99)/(90)`

`y=1.1`

So therefore you get the two costs by using the substitution method!

~~~~Best!!!