Question

on her way to work, lily purchases a coffee from starbucks. she adds $\frac{1}{2}$ oz of half-and-half, a mixture that is half cream and half milk, to her cup. because of her high cholesterol, she only allows herself $\frac{2}{3}$ oz of cream per day. what fraction of her daily allowance of cream does this drink contain?

Answer 1

The drink contains
`(3)/(8)` of Lily's daily allowance of cream.

Let's first find out how much cream Lily adds to her coffee, and then we can express it as a fraction of her daily allowance.

The half-and-half mixture is half cream and half milk. Since Lily adds
`\( (1)/(2) \)` oz of this mixture to her coffee, the amount of cream in this mixture is:

`\[ (1)/(2) * (1)/(2) \]` =
`(1)/(4)` oz

Now, we want to express
`\( (1)/(4) \)` oz of cream as a fraction of Lily's daily allowance, which is
`\( (2)/(3) \)` oz.

So, the fraction of her daily allowance that this drink contains is:

`\[ ((1)/(4))/((2)/(3)) \]`

Multiplying by its reciprocal:

`\[ (1)/(4) * (3)/(2) \]`

Now, multiply the numerators and denominators:

`\[ (1 * 3)/(4 * 2) = (3)/(8) \]`

Therefore, the drink contains
`\( (3)/(8) \)` of Lily's daily allowance of cream.