A carpenter purchased 50 ft of redwood and 70 ft of pine for a total cost of $258. A second purchase, at the same prices, included 90 ft of redwood and 60 ft of pine for a total cost of $372. Find the cost per foot of redwood and of pine.

Step-by-step explanation:

The two purchases can be described by the equations ...

  50r +70p = 258

  90r +60p = 372

Rewriting these equations in general form facilitates the use of the cross-multiplication method of solving them.

  50r +70p -258 = 0

  90r +60p -372 = 0

According to the cross-multiplication method, we need three cross-products:

  ∆1 = (50)(60) -(90)(70) = -3300

  ∆2 = (70)(-372) -(60)(-258) = -10560

  ∆3 = (-258)(90) -(-372)(50) = -4620

The solutions are the solutions to the equations ...

  1/∆1 = t/∆2 = p/∆3

  r = ∆2/∆1 = -10560/-3300 = 3.20

  p = ∆3/∆1 = -4620/-3300 = 1.40

The cost per foot of the redwood was $3.20; of the pine, $1.40.

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Additional comment

Here's how this version of the "cross-multiplication" method works. For equations ...

a coefficient array can be written as ...

The cross-products of interest are formed from adjacent columns:

and the solutions are ...

Using this method requires no more arithmetic operations than solving by substitution or elimination, and may require fewer: 6 products, 3 sums, and 2 quotients are needed.

y= -

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation: