Answer:
(35/6) spoons of syrup would be needed.
Step-by-step explanation:
First, we make the conversion of the measures from mixed numbers to fractions.
3 1/2 spoons
[tex]3\frac{1}{2}=3+\frac{1}{2}=\frac{\frac{2}{1}\ast3+\frac{2}{2}\ast1}{2}=\frac{6+1}{2}=\frac{7}{2}[/tex]3 3/5 gallons
[tex]3\frac{3}{5}=3+\frac{3}{5}=\frac{\frac{5}{1}\ast3+\frac{5}{5}\ast3}{5}=\text{ }\frac{15+3}{5}=\frac{18}{5}[/tex]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:
[tex]\frac{18}{5}\ast x=6\ast\frac{7}{2}[/tex][tex]\frac{18\ast x}{5}=\frac{6\ast7}{2}[/tex][tex]\frac{18x}{5}=\frac{42}{2}[/tex][tex]\frac{18x}{5}=21[/tex][tex]x=\frac{21\ast5}{18}[/tex]Now, we simplify by 3;
[tex]x=\frac{35}{6}[/tex](35/6) spoons of syrup would be needed.
