Respuesta :
so the students mad 4 and 1/2 quarts of soup.
they served 4/5 of that 4 and 1/2 to some friends....well, what's 4/5 of 4 and 1/2? well is just their product.
[tex]\bf 4\frac{1}{2}\implies \cfrac{4\cdot 2+1}{2}\implies \cfrac{9}{2}\qquad\qquad \qquad \qquad \cfrac{9}{2}\cdot \cfrac{4}{5}\implies \cfrac{18}{5}[/tex]
so, each friend got to drink 3/5 quart, how many servings, and therefore friends, can one get out of 18/5 quarts of soup?
well, how many times does 3/5 go into 18/5? let's check.
[tex]\bf \cfrac{\quad \frac{18}{5}\quad }{\frac{3}{5}}\implies \cfrac{18}{\underline{5}}\cdot \cfrac{\underline{5}}{3}\implies \cfrac{18}{3}\implies \stackrel{servings}{6}[/tex]
so, there were 6 servings, meaning there were 6 friends about.
now, whatever happened to Hector? well, 18/5 in mixed is 3 and 3/5, so he's correct, there were 3 and 3/5 "quarts in total" served to the friends, but each serving wasn't that much, was just a fraction of that.
they served 4/5 of that 4 and 1/2 to some friends....well, what's 4/5 of 4 and 1/2? well is just their product.
[tex]\bf 4\frac{1}{2}\implies \cfrac{4\cdot 2+1}{2}\implies \cfrac{9}{2}\qquad\qquad \qquad \qquad \cfrac{9}{2}\cdot \cfrac{4}{5}\implies \cfrac{18}{5}[/tex]
so, each friend got to drink 3/5 quart, how many servings, and therefore friends, can one get out of 18/5 quarts of soup?
well, how many times does 3/5 go into 18/5? let's check.
[tex]\bf \cfrac{\quad \frac{18}{5}\quad }{\frac{3}{5}}\implies \cfrac{18}{\underline{5}}\cdot \cfrac{\underline{5}}{3}\implies \cfrac{18}{3}\implies \stackrel{servings}{6}[/tex]
so, there were 6 servings, meaning there were 6 friends about.
now, whatever happened to Hector? well, 18/5 in mixed is 3 and 3/5, so he's correct, there were 3 and 3/5 "quarts in total" served to the friends, but each serving wasn't that much, was just a fraction of that.
The correct number of servings of soup is 6.
What Hector did wrong was that he assumed that the total quarts that was served is the number of servings.
The first step to determine the answer is to determine the total quarts of soup that was served.
Quarts served = fraction served x quarts the class made
[tex]\frac{4}{5}[/tex] × [tex]4\frac{1}{2}[/tex]
[tex]\frac{4}{5}[/tex] × [tex]\frac{9}{2}[/tex] = [tex]\frac{18}{5}[/tex] = [tex]3\frac{3}{5}[/tex]
The second step is to determine the number of servings. In order to determine the number of servings, divide the quart of each serving by the total quarts served.
[tex]\frac{18}{5}[/tex] ÷ [tex]\frac{3}{5}[/tex]
[tex]\frac{18}{5}[/tex] × [tex]\frac{5}{3}[/tex] = 6 servings
A similar question was answered here: https://brainly.com/question/14303039?referrer=searchResults
