The value of an antique mirror increased by 40% since juliet bought it. its value is now $350. what amount did juliet originally pay for the mirror.

The problem states that the current value is $350 and that is the original price plus 40%, that is $350 is the 140%, the question is how much is the 100%, or the original price, lets use a rule of three, simple, direct proportion:
140% > $350
100% > x
x = (100)(350)/140
x = 250
that is the original price, $250

X would equal 15. 7x = 5x + 30. Subtract 5x from both sides then divide by 2. X=15