<PRE><B>Question 1191411</B>
x equals the new price.
y equals the old price.
x = y + 6
2/3 * x = 5/7 * y
multiply both sides of this equation by 3/2 to get:
x = 5/7 * 3/2 * y
simplify to get:
x = 15/14 * y
since x = y + 6, then you get:
y + 6 = 15/14 * y
subtract y from both sides of the equation to get:
6 = 15/14 * y - y
since 1 * y = 14 * y / 14, you get:
6 = 15/4 * y - 14/14 * y
simplify to get:
6 = 1/14 * y
solve for y to get:
y = 14 * 6 = 84
since x = y + 6, then you get:
x = 90
to confirm, you have:
x = y + 6 becomes 90 = 84 + 6 which is true.
2/3 * x = 5/7 * y becomes 2/3 * 90 = 5/7 * 84 which becomes 60 = 60 which is true.
this confirms the solution is correct.
the solution is that the new price is $90 per liter.



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