$670 = cost + 35%(cost) = cost(1 + 35%) = cost(1 + .35)

$670 = 1.35*cost

$670/1.35 = cost = $496.30 (dividing both sides of the equation by 1.35)

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Check

cost = $496.30

35% of cost = profit = 35%(496.30) = $173.70 (if you round down)

$496.30 + $173.70 = $670.00

173.70/496.30 = 34.999%

$670 = 1.35*cost

$670/1.35 = cost = $496.30 (dividing both sides of the equation by 1.35)

_____

Check

cost = $496.30

35% of cost = profit = 35%(496.30) = $173.70 (if you round down)

$496.30 + $173.70 = $670.00

173.70/496.30 = 34.999%