Answer:
3 mL of hot sauce mixed with 2 ounces of barbecue sauce
45 mL of hot sauce mixed with 30 ounces of barbecue sauce
12 mL of hot sauce mixed with 8 ounces of barbecue sauce
Step-by-step explanation:
we know that
A restaurant makes a dipping sauce with
![\frac{9}{6}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B6%7D%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
Simplify
![1.5\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=1.5%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
<u><em>Verify each case</em></u>
case A) we have
6 mL of hot sauce mixed with 10 ounces of barbecue sauce
so
![\frac{6}{10}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B10%7D%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
simplify
![0.6\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=0.6%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
Compare
![0.6 \neq 1.5](https://tex.z-dn.net/?f=0.6%20%5Cneq%201.5)
therefore
This mixture is not the same that as Flaming BBQ's dipping sauce
case B) we have
3 mL of hot sauce mixed with 2 ounces of barbecue sauce
so
![\frac{3}{2}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
simplify
![1.5\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=1.5%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
Compare
![1.5 =1.5](https://tex.z-dn.net/?f=1.5%20%3D1.5)
therefore
This mixture is the same that as Flaming BBQ's dipping sauce
case C) we have
45 mL of hot sauce mixed with 30 ounces of barbecue sauce
so
![\frac{45}{30}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=%5Cfrac%7B45%7D%7B30%7D%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
simplify
![1.5\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=1.5%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
Compare
![1.5=1.5](https://tex.z-dn.net/?f=1.5%3D1.5)
therefore
This mixture is the same that as Flaming BBQ's dipping sauce
case D) we have
24 mL of hot sauce mixed with 18 ounces of barbecue sauce
so
![\frac{24}{18}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=%5Cfrac%7B24%7D%7B18%7D%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
simplify
![1.33\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=1.33%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
Compare
![1.33 \neq 1.5](https://tex.z-dn.net/?f=1.33%20%5Cneq%201.5)
therefore
This mixture is not the same that as Flaming BBQ's dipping sauce
case E) we have
12 mL of hot sauce mixed with 8 ounces of barbecue sauce
so
![\frac{12}{8}\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B8%7D%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
simplify
![1.5\ \frac{mL\ hot\ sauce}{oz\ barbecue\ sauce}](https://tex.z-dn.net/?f=1.5%5C%20%5Cfrac%7BmL%5C%20hot%5C%20sauce%7D%7Boz%5C%20barbecue%5C%20sauce%7D)
Compare
![1.5=1.5](https://tex.z-dn.net/?f=1.5%3D1.5)
therefore
This mixture is the same that as Flaming BBQ's dipping sauce