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a custom fencing company sold 2000 feet of pasture fencing and 450 feet of picket fencing for a total of $12,850. the next week, at the same price, the fencing company sold 700 feet of pasture fencing and 300 feet of picket fencing for a total of $6,350. find the cost per foot of the picket fencing.

  $13.00

Step-by-step explanation:

Let f represent the price per foot of pasture fence, and p represent the price per foot of picket fence. The two purchases can be written in equation form as ...

  2000f + 450p = 12850

  700f +300p = 6350

Using Cramer's rule, we can find the value of the picket fence as ...

  p = (12850·700 -6350·2000)/(450·700 -300·2000) = -3705000/-285000

  p = 13

The cost per foot of picket fence is $13.00.

Cramer's Rule and Vedic math

The above equation for p is a summary of the math you would be doing if you were to solve the equations by eliminating f. Cramer formulates it in terms of determinants of the coefficients in the equations. Practitioners of Vedic math formulate it in terms of X-pattern combinations of the coefficients in much the same way as finding a determinant. For the equations ...

The solutions are ...

  ∆ = bd -ea

  x = (bf -ec)/∆

  y = (cd -fa)/∆ . . . . . this is the equation we used above

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If you do a rigorous comparison of this formula with that of Cramer's rule, you find the signs of numerator and denominator are reversed. That has no net effect on the solution, but it makes the X pattern of products easier to remember for practitioners of Vedic math.