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dybincka [34]
3 years ago
13

A coffeepot contains 1 1/2 quqarts of coffee. After Tonya pours an equal amount of coffee into two cups, 3 1/2 cups of coffee st

ill remain in the pot. How much coffee did Tonya pour into each cup?
Mathematics
1 answer:
saw5 [17]3 years ago
5 0
\bf 1\frac{1}{2}\implies \cfrac{1\cdot 2+1}{2}\implies \cfrac{3}{2}\quad \textit{now, how much is a quart of that?}
\\\\\\
\cfrac{3}{2}\cdot \cfrac{1}{4}\implies \stackrel{of~coffee}{\cfrac{3}{8}}\impliedby makes\quad \stackrel{poured}{2cups}+\stackrel{remaining}{3\frac{1}{2}cups}\implies 5\frac{1}{2}~cups

\bf \textit{now if }\frac{3}{8}\textit{ of coffee makes }5\frac{1}{2}\textit{ cups, how much in 1 cup?}
\\\\\\
\cfrac{\quad \frac{3}{8}\quad }{5\frac{1}{2}}\implies \cfrac{\quad \frac{3}{8}\quad }{\frac{5\cdot 2+1}{2}}\implies \cfrac{\quad \frac{3}{8}\quad }{\frac{11}{2}}\implies \cfrac{3}{8}\cdot \cfrac{2}{11}\implies \stackrel{\textit{of coffee makes one cup}}{\cfrac{3}{44}}
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We are given function: y= - 5.131x^2+ 31.821x - 3.333

Where, x is the number of hours after 5a.m.

We need to approximates the number of people standing in line to catch a commuter train at 7 a.m.

From 5 a.m. to 7 a.m. total number of hours = 7-5 = 2 hours.

So, we need to plug x=2 in the given function.

Plugging x=2 in y=- 5.131x^2+ 31.821x - 3.333, we get

y=- 5.131(2)^2+ 31.821(2) - 3.333

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