My Math Forum System of equations (practical problem)

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 July 25th, 2014, 07:05 PM #1 Newbie   Joined: Jul 2014 From: Mexico Posts: 2 Thanks: 0 System of equations (practical problem) It looks like a simple problem but I'm not sure how to going on. In a pastry class each student prepare a dough of water and flour weighing 8 ounces. The amounts of flour and water for each student were varied but never 0. One student spent one quarter of the available water and 1/6 of the available flour. How many students were in the class? My attempt: $$\frac{1}{4}mass_{water} + \frac{1}{6}mass_{flour} = 8 \\ \frac{3}{4}mass_{water} + \frac{5}{6}mass_{flour} = 8 \times(n-1),$$ being $n$ the number of students. It seems that I need one equation more. What do you think? Last edited by dapias09; July 25th, 2014 at 07:07 PM.
July 25th, 2014, 07:53 PM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
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Hello, dapias09!

You're off to a good start.

Quote:
 In a pastry class, each student prepares a dough of water and flour weighing 8 ounces. The amounts of flour and water for each student were varied but never 0. One student spent one quarter of the available water and 1/6 of the available flour. How many students were in the class?

Let $n$ = number of students.

$\quad \frac{1}{4}W + \frac{1}{6}F \:=\:8$

$\quad \frac{3}{4}W + \frac{5}{6}F \:=\:8(n-1)$

I cleared out the fractions:

$\quad 3W + 2F \:=\:96$

$\quad 9W + 10F \:=\:96n-96$

I solved the system: $\begin{Bmatrix}W &=& 96 - 16n \\ F &=& 24n - 96\end{Bmatrix}$

Since $W > 0$, we have: $\:96-16n \:>\:0 \quad\Rightarrow\quad n \:<\:6$

Since $F > 0$, we have: $\: 24n - 96 \:>\:0 \quad\Rightarrow\quad n \:>\:4$

Therefore: $\:n \:=\:5.$

 July 26th, 2014, 07:11 AM #3 Newbie   Joined: Jul 2014 From: Mexico Posts: 2 Thanks: 0 Hello soroban, thank you very much, your explanation makes sense for me

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