Question

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) 15/29b) 5/8c) 5/16d) 1/2e) 13/27

Answer 1

a) 15/29

Step-by-step explanation:

The fraction in which the olive oil must be added = 5 / 8

Vinegar's fraction = 1 / 4

The remainder is =
`1-\frac {5}{8}-\frac {1}{4}` = 1 / 8

Salt, pepper and sugar are mixed evenly. SO,

Salt's fraction = Pepper's fraction = Sugar's fraction = 1 / 24

Thus, New recipe contains:

Olive oil's fraction = 5 / 8

He doubles the vinegar, So, Vinegar's fraction = 1 / 2

He missed sugar, so left ones are salt and pepper which are:

Salt's fraction = Pepper's fraction = 1 / 24

Total = (5 / 8) + (1 / 2) + (1 / 24) + (1 / 24) = 29 / 24

Olive oil's proportion =
`\frac {Amount\ of\ Olive\ oil}{Total\ amount}=\frac {\frac {5}{8}}{\frac {29}{24}}=\frac {5}{8}* \frac {24}{29}` = 15 / 29