Question

Taisha and Shakina are each making punch. Taishas recipe calls for 5 parts pineapple juice to 3 parts sherbet. Shakira’s recipe calls for 8 parts pineapple juice to 6 parts orange sherbet. Which recipe will have a stronger orange sherbet flavor?

Answer 1

1.the first recipe contains: 5 parts / pineapple juice ; for 3 parts / orange sherbet;

2.the second recipe has: 8 parts / pineapple juice, for 6 parts of orange sherbet.

we will formulate proportions to find real values,

then;

`\begin{gathered} (x)/(5)=(z)/(3)\text{ }=\text{ }(x)/(5)\text{ }+(z)/(3)=(100)/(8)\text{ first recipe} \\ (x)/(5)\text{ }=(100)/(8)=\text{ x }=100*5/8=62.5\text{ pineapple juice} \\ \text{ Now } \\ (z)/(3)\text{ }=(100)/(8)\text{ }=\text{ z}=100*3/8=37.5\text{ orange sherbet in the }first\text{ recipe} \\ \text{second recipe;} \\ (y)/(8)=(b)/(6)\text{ }=(y)/(8)+(b)/(6)\text{ }=(100)/(14) \\ (y)/(8)=(100)/(14)=y=100*8/14=57.14\text{ pineapple juice} \\ (b)/(6)=(100)/(14)=b\text{ }=100*6/14=42.85\text{ orange sherbet in the second recipe} \\ \text{Now we }compare\text{ both result,} \\ \text{first recipe: 37.5 orange sherbet} \\ \text{second recipe.42.85 orange sherbet;} \\ \text{then }the\text{ recipe w}hich\text{ }is\text{ more orange flavor is the second recipe.} \\ \\ \end{gathered}`

In the exercise we had to find exactly the real value of each ingredient, for that, proportions of each recipe were made, different variables were applied for both the first and second recipes. At the end, the values ​​obtained were compared.