Answer: The quantity of sugar that the baker use is 306 pounds.
Step-by-step explanation: Given that a baker mixes [tex]2\frac{1}{4}[/tex] pounds of sugar for every [tex]\frac{3}{8}[/tex] pound of butter to begin making frosting.
The baker uses 357 pounds of butter and sugar to start the frosting.
We are to find the quantity of sugar that the baker use.
Let x pounds and y pounds be the respective quantities of sugar and butter that the baker use.
Then, according to the given information, we have
[tex]x:y=2\dfrac{1}{4}:\dfrac{3}{8}\\\\\\\Rightarrow x:y=\dfrac{9}{4}:\dfrac{3}{8}\\\\\\\Rightarrow \dfrac{x}{y}=\dfrac{\frac{9}{4}}{\frac{3}{8}}\\\\\\\Rightarrow \dfrac{x}{y}=\dfrac{9\times8}{4\times3}\\\\\\\Rightarrow \dfrac{x}{y}=6\\\\\Rightarrow y=\dfrac{x}{6}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]x+y=357\\\\\Rightarrow x+\dfrac{x}{6}=357~~~~~~~~~~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\\Rightarrow \dfrac{6x+x}{6}=357\\\\\Rightarrow 7x=357\times6\\\\\Rightarrow x=\dfrac{357\times6}{7}\\\\\Rightarrow x=51\times6\\\\\Rightarrow x=306.[/tex]
Thus, the quantity of sugar that the baker use is 306 pounds.
