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3 years ago

A punch recipe calls for orange juice and pop in the ratio of 2:5 the recipe requires 1L of Pop to serve 7 people

Mathematics

1 answer:

nordsb [41]3 years ago

5 0

O : P => 2 : 5

(a) 1 liter of pop to serve 7 people

=> 5 units = 1

1 unit = 1 / 5

Orange juice => 2 units

Hence, Orange juice needed is 2 * 1 / 5 = 0.4 liters

(b) If 1 liter of pop is needed to serve 7 people, then we will need (1 / 7) * 15 for 15 people

i.e. 2.14 liters

As the ratio of O : P = 2 : 5,

5 units = 2.14

1 units = 2.14 / 5

For Orange juice, we will need 2 * 2.14 / 5 = 0.856 liters for 15 people

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cricket20 [7]

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$\begin{array}{ccc}x_1&=&-x_3\\x_2&=&-x_3\\x_3&=&arbitrary\end{array}$

Step-by-step explanation:

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There are three elementary matrix row operations:

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$\begin{array}{ccccc}x_1&-3x_2&-2x_3&=&0\\-x_1&2x_2&x_3&=&0\\2x_1&+3x_2&+5x_3&=&0\end{array}$

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$\left[ \begin{array}{cccc} 1 & -3 & -2 & 0 \\\\ -1 & 2 & 1 & 0 \\\\ 2 & 3 & 5 & 0 \end{array} \right]$

This matrix can be transformed by a sequence of elementary row operations

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Row Operation 2: add -2 times the 1st row to the 3rd row

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Row Operation 4: add -9 times the 2nd row to the 3rd row

Row Operation 5: add 3 times the 2nd row to the 1st row

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$\left[ \begin{array}{cccc} 1 & 0 & 1 & 0 \\\\ 0 & 1 & 1 & 0 \\\\ 0 & 0 & 0 & 0 \end{array} \right]$

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$\left[ \begin{array}{cccc} 1 & 0 & 1 & 0 \\\\ 0 & 1 & 1 & 0 \\\\ 0 & 0 & 0 & 0 \end{array} \right]$

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$\begin{array}{ccccc}x_1&&-x_3&=&0\\&x_2&+x_3&=&0\\&&0&=&0\end{array}$

The system has infinitely many solutions.

$\begin{array}{ccc}x_1&=&-x_3\\x_2&=&-x_3\\x_3&=&arbitrary\end{array}$

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