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A carpenter purchased 50 ft of redwood and 70 ft of pine for a total cost of $280. A second purchase, at the same prices, included 100 ft of redwood and 60 ft of pine for a total cost of $440. Find the cost per foot of redwood and of pine.

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adioabiola

The cost per foot of redwood and of pine is $3.5 and $1.5 respectively.

How to solve simultaneous equation?

let

  • cost of redwood = x
  • cost of pine = y

50x + 70y = 280

100x + 60y = 440

Multiply (1) by 2

100x + 140y = 560

100x + 60y = 440

subtract to eliminate x

80y = 120

y = 120/80

y = $1.5

substitute y = 1.5 into (1)

50x + 70y = 280

50x + 70(1.5) = 280

50x + 105 = 280

50x = 280 - 105

50x = 175

x = 175 / 50

x = $3.5

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