She uses 9 ounces of cocoa to make the hot chocolate.
If the ratio of cocoa to the total mixture is 1:8, and the total mixture is 32 ounces, you can find the amount of cocoa by dividing the total mixture by the sum of the parts in the ratio (1 + 8).
Let
represent the number of parts of cocoa.
The ratio of cocoa to the total mixture is 1:8, which means
.
The total number of parts is 1 + 8 = 9.
Now, set up an equation:
![\[ (x)/(9) \cdot 32 = \text{amount of cocoa} \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/beeob0aeozlt8thyv8o2b35bin8rnqt1k5.png)
Solve for x:
![\[ x = (9)/(32) \cdot \text{amount of cocoa} \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/ha2i4s9nq9qr20z71vfjvi2lqpp9c15gdr.png)
Now, substitute the given values:
![\[ x = (9)/(32) \cdot 32 \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/jyu9eboid6fn1gt9c3inmaawtmjihfrwey.png)
Simplify:
x = 9
So, she uses 9 ounces of cocoa to make the hot chocolate.
The probable question may be:
"Do you make a large batch of hot chocolate the way she likes it when she is done mixing she has a total of 32 ounces of hot chocolate how many ounces of cocoa does she use to make the ratio 1:8"