To determine the ratio of full-cream milk sold to standard milk sold, let's analyze the information provided:
1. Identify Portions Sold:
- Standard milk: [tex]\(\frac{1}{3}\)[/tex] of the total milk sold.
- Low-fat milk: [tex]\(\frac{1}{2}\)[/tex] of the total milk sold.
2. Calculate Full-Cream Milk Portion:
- The sum of the portions of standard milk and low-fat milk is:
[tex]\[
\frac{1}{3} + \frac{1}{2} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6}
\][/tex]
- The portion of full-cream milk sold is what remains out of the total, which is:
[tex]\[
1 - \frac{5}{6} = \frac{1}{6}
\][/tex]
3. Determine the Ratio of Full-Cream Milk to Standard Milk:
- The portion of full-cream milk is [tex]\(\frac{1}{6}\)[/tex].
- The portion of standard milk is [tex]\(\frac{1}{3}\)[/tex].
- To find the ratio, we divide the portion of full-cream milk by the portion of standard milk:
[tex]\[
\text{Ratio} = \frac{\frac{1}{6}}{\frac{1}{3}} = \frac{1}{6} \times \frac{3}{1} = \frac{1 \times 3}{6 \times 1} = \frac{3}{6} = \frac{1}{2}
\][/tex]
- Thus, the ratio of full-cream milk sold to standard milk sold is [tex]\(1:2\)[/tex].
So, the correct answer is: [tex]\(1:2\)[/tex].
