Question

going to halibut seasoning at Captain Cleo's fish shop calls for 1/4 teaspoon of paprika for every 3 1/2 tsp. of salt. if there is 1/2 tsp. of paprika, how many tsp. of salt?

Answer 1

First, we must convert the mixed fraction 3 1/2 into a simple fraction form:

`3(1)/(2)=(2\cdot3+1)/(2)=(7)/(2)`

and now, we can apply the rule of three as

`\begin{gathered} (1)/(4)\text{tsp paprika ------- }(7)/(2)tsp.\text{salt} \\ (1)/(2)\text{tsp paprika ------- x} \end{gathered}`

then, x is given by

`x=(((1)/(4))((7)/(2)))/((1)/(2))`

the x is given by

`\begin{gathered} x=((1\cdot7)/(4\cdot2))/((1)/(2)) \\ x=((7)/(8))/((1)/(2)) \end{gathered}`

now, by appliying the sandwich law, we have

`\begin{gathered} x=(7\cdot2)/(8\cdot1) \\ x=(14)/(8) \end{gathered}`

this last result is equivalente to

`x=(7)/(4)`

in other words, we need 7/4 tsp of salt for 1/2 tsp of paprika.