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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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
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
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
teaspoons and tablespoons are not interchangeable units :-)