In cooking, 1 drop is equal to 1/6 of a dash. if a recipe calls for 2/3 of a dash, write an expression that would give the number of drops that are needed

Remark

You need only set up a proportion

Use the given first. Then let x = the number of drops.

1 drop / (1/6 dash) = x / (2/3 dash)

Rather than try and figure out what the fractions are going to do, why not change everything to decimals?

1/0.16666667 = x /0.6666667          multiply both sides by 0.6666667

1 * 0.6666667 / 0.16666667 = x

x = 4. That's the answer you would get if you kept the fractions. But decimals are much easier to handle in cases like this than are fractions.

If you want this in terms of genenerally how many drops would there be then

y = (1/6)*x <<< Answer

Where y is the number of dashes and x is the number of drops. 

-8/2y-8=5/y+4-7y+8/y^2-16

we move all terms to the left:

-8/2y-8-(5/y+4-7y+8/y^2-16)=0

we can not solve this equation

ok thats very interesting