noodlesalad wrote:
Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
A. 15/29
B. 5/8
C. 5/16
D. 1/2
E. 13/27
Official Solution (Credit: Manhattan Prep)
This problem can be solved most easily by picking smart numbers and assigning values to the portion of each ingredient in the dressing. A smart number in this case would be one that enables you to add and subtract ingredients without having to deal with fractions or decimals. In a fraction problem, the ‘smart number’ is typically based on the least common denominator among the given fractions.
The two fractions given, 5/8 and 1/4, have a least common denominator of 8. However, we must also consider the equal parts salt, pepper and sugar. Because 1/4 = 2/8, the total proportion of oil and vinegar combined is 5/8 + 2/8 = 7/8. The remaining 1/8 of the recipe is split three ways: 1/24 each of salt, pepper, and sugar. 24 is therefore our least common denominator, suggesting that we should regard the salad dressing as consisting of 24 units. Let’s call them cups for simplicity, but any unit of measure would do. If properly mixed, the dressing would consist of
5/8 × 24 = 15 cups of olive oil
1/4 × 24 = 6 cups of vinegar
1/24 × 24 = 1 cup of salt
1/24 × 24 = 1 cup of sugar
1/24 × 24 = 1 cup of pepper
Miguel accidentally doubled the vinegar and omitted the sugar. The composition of his bad salad dressing would therefore be
15 cups of olive oil
12 cups of vinegar
1 cup of salt
1 cup of pepper
The total number of cups in the bad dressing equals 29. Olive oil comprises 15/29 of the final mix.
The correct answer is A.