Alright, let's solve this problem step-by-step.
1. Convert the mixed fraction price per rune into a single fraction:
Given: [tex]\( \frac{16}{16} \frac{3}{4} \)[/tex]
The mixed fraction can be interpreted as [tex]\(16 + \frac{3}{4}\)[/tex]. To find the cost per rune, we need to divide this amount by 16.
[tex]\[
\frac{16 + \frac{3}{4}}{16}
\][/tex]
[tex]\(16 + \frac{3}{4}\)[/tex] is equal to [tex]\(16.75\)[/tex].
Then, the cost per rune can be found by dividing 16.75 by 16:
[tex]\[
16.75 / 16 = 1.046875
\][/tex]
So, the cost of milk per rune is [tex]\(1.046875\)[/tex].
2. Convert the mixed fraction quantity of milk into a single fraction:
Given: [tex]\(6 \frac{2}{6}\)[/tex]
The mixed fraction can be interpreted as [tex]\(6 + \frac{2}{6}\)[/tex]. To simplify this:
[tex]\[
6 + \frac{2}{6} = 6 + 0.3333333333333333 \approx 6.333333333333333
\][/tex]
So, the amount of milk in runes is [tex]\(6.333333333333333\)[/tex].
3. Calculate the total cost:
Now we use both the cost per rune and the total quantity of milk to find the total cost:
[tex]\[
\text{Total cost} = \text{Cost per rune} \times \text{Quantity of milk}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Total cost} = 1.046875 \times 6.333333333333333
\][/tex]
By performing the multiplication:
[tex]\[
\text{Total cost} \approx 6.630208333333333
\][/tex]
So, the cost of [tex]\(6 \frac{2}{6}\)[/tex] runes of milk is approximately [tex]\(6.630208333333333\)[/tex] runes.
