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- anonymous

Hanna makes her own furniture polish using thirty percent vinegar and seventy percent olive oil. Write and solve an equation to determine how much total solution she made if she used fourteen tablespoons of olive oil. Show your work.

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- jim_thompson5910

Let x = amount of vinegar
if she wants to make a solution that's 30% vinegar and 70% olive oil, then you would need to make the ratio x/(x+14) equal to 0.3
this is because x/(x+14) is the percentage of x teaspoons of vinegar out of the total amount x+14 teaspoons
this means...
x/(x+14) = 0.3
x = 0.3(x+14)
x = 0.3x+0.3*14
x = 0.3x+4.2
x - 0.3x = 4.2
0.7x = 4.2
x = 4.2/0.7
x = 6
So she needs 6 teaspoons of vinegar

- jim_thompson5910

If she has 6 teaspoons of vinegar and fourteen tablespoons of olive oil, then she will have 6+14 = 20 teaspoons of solution
the percentage of vinegar is 6/20 = 0.3 = 30%
the percentage of olive oil is 14/20 = 0.7 = 70%
so that checks out

- whpalmer4

teaspoons and tablespoons are not interchangeable units :-)

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- jim_thompson5910

oh my bad, but you get the idea
just replace all teaspoons with tablespoons

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