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

Answer:

Redwood: $3.50 per foot

Pine: $1.10 per foot

Step-by-step 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)

$90y=274-50x$

$\frac{90y}{90} =\frac{274}{90} -\frac{50x}{90}$

$y=\frac{274}{90} -\frac{50x}{90}$

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

$80x+50(\frac{274}{90} -\frac{50x}{90})=335$

$80x+152.2-27.8x=335$

$80x-27.8x=182.8$

$\frac{52.2x}{52.2} =\frac{182.8}{52.2}$

$x=3.50$

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).

$50(3.5)+90y=274$

$175+90y=274$

$\frac{90y}{90}=\frac{99}{90}$

$y=1.1$

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

~~~~Best!!!