Question

It takes 3 1/2 spoons of chocolate syrup to make 3 3/5 gallons of chocolate milk. How many spoons of syrup would it take to make 6 gallons of chocolate milk?

Answer 1

(35/6) spoons of syrup would be needed.

Explanation:

First, we make the conversion of the measures from mixed numbers to fractions.

3 1/2 spoons

`3(1)/(2)=3+(1)/(2)=((2)/(1)\ast3+(2)/(2)\ast1)/(2)=(6+1)/(2)=(7)/(2)`

3 3/5 gallons

`3(3)/(5)=3+(3)/(5)=((5)/(1)\ast3+(5)/(5)\ast3)/(5)=\text{ }(15+3)/(5)=(18)/(5)`

Now, we make a rule of three.

For 7/2 spoons, we need 18/5 gallons.

How many spoons for 6 gallons?

7/2 spoons - 18/5 gallons

x spoons - 6 gallons.

Applying cross multiplication:

`(18)/(5)\ast x=6\ast(7)/(2)`
`(18\ast x)/(5)=(6\ast7)/(2)`
`(18x)/(5)=(42)/(2)`
`(18x)/(5)=21`
`x=(21\ast5)/(18)`

Now, we simplify by 3;

`x=(35)/(6)`

(35/6) spoons of syrup would be needed.