Question

Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

Answer 1

16 cups of salad dressings can be prepared by the ingredients available.

Explanation:

It is given that Oil, vinegar and water are mixed in a ratio of 3 : 2 : 1.

Larry has 8 cups of oil, 7 cups of vinegar and access of water to prepare the maximum numbers of cups of salad dressing.

Let the number of oil used = 8 cups

then the number of cups of vinegar used will be in the ratio of 3 : 2,

`\frac{\text{Oil}}{\text{Vinegar}}=(3)/(2)`

`\frac{8}{\text{Vinegar}}=(3)/(2)`

`\text{Vinegar}=(2* 8)/(3)`

`\text{Vinegar}=(16)/(3)` cups

Similarly, number of cups of water can be used in the ratio of 2 : 1,

`\frac{\text{Vinegar}}{\text{Water}}=(2)/(1)`

`\frac{(16)/(3)}{\text{Water}}=(2)/(1)`

`\frac{16}{3* \text{Water}}=2`

`\text{Water}=(16)/(6)`

`\text{Water}=(8)/(3)` cups

So total number of salad dressing prepared will be =
`8+(16)/(3)+(8)/(3)`

=
`8+((16+8))/(3)`

= 8 + 8

= 16 cups

Therefore, 16 cups of salad dressings can be prepared by the ingredients available.